This build focuses on building Jaina to her fullest offensive potential. This is also my first guide (ever), so please be considerate.

Jaina is a ranged mage (assassin) that uses spells to slow and burst down enemies. She is one of the strongest offensive heroes in the game, but is also considered to be one of the 'squishiest', that is easily killed.

Trait

Frostbite is Jaina's combat trait. This trait grants 50% ability damage to chilled targets, that is targets that have already been hit by an ability, as well as slows targets by 25% (lasts 4 seconds). By combo'ing abilities together, Jaina can output some ridiculous damage through this trait.

Abilities

Frostbolt is Jaina's skillshot. It's low cooldown, comparative to her other abilities, make it a great initiate to inflict single target damage.

Blizzard is one of Jaina's AoE spells. It is a circular spell that hits an area with two waves of damage after an initial 1 second delay. This ability provides a lot of Jaina's ability damage, and is quite useful when enemies are clustered, rooted, or slowed in one area.

Cone of Cold is Jaina's other AoE spell. This aptly named spell hits targets in a cone-shaped area for moderate damage. This spell is great to initiate fights against multiple targets due to it being an instantaneous spell that will apply frostbite to all targets hit.

Heroic (Ultimate) Abilities

Ring of Frost is one of Jaina's Heroic abilities. This ability creates a ring that roots and damages enemies for 3 seconds. It is considered to be the 'weaker' heroic due to the difficulty of landing it successfully.

Summon Water Elemental is Jaina's other Heroic ability. This ability summons a powerful water elemental to fight opponents. This heroic is widely considered to be the 'stronger' heroic due to it's high damage output, ability to chill all targets hit, splash damage, and retargeting ability.

Positioning Side Note

The most important aspect to maintain while playing Jaina is positioning. You need to always be aware of what is going on around you, and more specifically where other heroes (both friendly and enemy) are. The last thing you want to happen is for a sneaky Zeratul or Nova to find you when you're all alone and make you go poof. With this build, the difference between an average Jaina player and a great Jaina player is how you position yourself.
Here are some tips:

Try to stay behind minion waves in the early game
Be aware of how far you are from friendly gates/towers
Don't get caught transitioning between lanes by yourself

Level 1

Preferred: Deep Chill
This talent increases the slow effect of Jaina's trait. As long as you are hitting targets with your abilities, they will continue to be slowed by 35%, which makes pursuing fleeing enemies easy.

Optional: Winter's Reach
This talent can be useful when you feel like you will need extra range to poke at targets. It could be argued that securing kills on fleeing enemies with the 30% extra range to abilities/frostbolt], but I think that the extra 10% slow from [[talent/deep-chill is a viable way to secure those kills, while providing more overall utility.

Avoid: Lingering Chill
While the extra 2 second application of chill seems like a great thing, I've found that 4 seconds is ample time to chase down targets and secure a kill. Slowing the target more (with Deep Chill) will result in more kills than slowing targets less but for more time with Lingering Chill.

Avoid: Conjurer's Pursuit
This talent is useful if you are having trouble conserving mana, but there is a much better talent at level 4 ( Arcane Intellect) that doesn't revolve around consistently grabbing regen globes.

Level 4

Preferred: Arcane Intellect
This talent is THE reason why this build works. Worried about running out of mana? Well, Arcane Intellect allows you to spam your abilities with little regard to no regard for your mana bar. Every time you attack a chilled opponent, some mana is returned to you.

For example: Spamming all of your abilities on a single target and then basic attacking for the full duration of chill (at 4 seconds) will cost around 30 mana at level 4. At level 10, even after summoning your water elemental, you will only spend about 60 mana.

Optional: Snowstorm
A lot of guides and builds for Jaina emphasize spec'ing into Blizzard. While increasing the width of Blizzard is certainly useful, I believe that more damage output can be achieved by using all of Jaina's abilities as often as possible than by upgrading one ability specifically.

Avoid: Frost Shards
To make this talent viable, you need to be spec'ing into Frostbolt. That being said, it is hard enough to land this skill shot consistently, let alone lining up two targets.

Avoid: Envenom
This used to be my selection at this level. It provided instant damage and seemed like a good choice. However, as I mentioned before, I prefer to spam abilities to burst people down. This talent has also seen a recent nerf, increasing the duration of envenom from 5 to 10 seconds, which is usually enough time for the victim to heal in some way.

Level 7

Preferred: Frostbitten
What's better than a 50% increase in damage to chilled targets? A 65% increase in damage to chilled targets! This talent allows even BIGGER burst to targets after initially chilling them with an ability.

Optional: Ice Floes
I rarely take this talent, but I can see its' worth. This can pair great with a level 16 talent ( Northern Exposure or Numbing Blast). Again, I usually opt for the increase in damage to chilled targets with Frostbitten, as it provides a damage increase to all abilities instead of just one.

Avoid: Frost Armor
For my build, I rely upon great positioning and an extremely bursty offense. Taking talents that give Jaina defense and escapes take away from her offensive potential. While chilling targets that attack you seems great, YOU want to be the one applying chill to THEM by using your spells.

Avoid: Ice Lance
The reduction in cooldown makes your frostbolt almost up instantaneously after casting it. Like I've mentioned a bunch before though, this makes one ability better, but is lacking due to it not helping all of your abilities as much.

Level 10

Preferred: Summon Water Elemental
As mentioned before, this is the superior heroic ability. The utility that this summon provides is incredible. While it can die rather quickly if focused, it is one of the most versatile ultimates in the game.

Avoid: Ring of Frost
This talent is particularly tricky to land. Not only is there ample time for enemy heroes to walk off the ring before it triggers, but it also doesn't do anything in the middle of the circle (unless you take Cold Snap). It can be useful for locking down enemies, but for this build it is not viable.

Level 13

Preferred: Icy Veins
Icy veins is like a less instant version of Rewind. It allows you to spam your abilities EVEN FASTER. Popping this talent as a fight breaks out, or even taking mercenary camps allows you to do immense damage. Taking Arcane Intellect for your level 4 talent helps alleviate the mana cost of spamming, even with the 50% reduction this talent gives.

Optional: Improved Ice Block
If you have found that you're getting blown up, heavily targeted, or maybe that your positioning has been particularly terrible, then this is the talent for you. If you're facing someone with backlining potential such as Illidan with [talent/the-hunt-talent]] or Tyrael with Judgment then this is almost must (assuming they're always targeting YOU). Just make sure you realize you're giving up a large amount of burst damage by taking this over Icy Veins, and will have a harder time contributing offensively to team fights and soloing mercenary camps.

Optional/Avoid: Storm Front
If you're going for a Blizzard build, then this is the talent for you. It's easy to get out of position with Jaina, especially when you're trying to land your abilities. This talent allows you to cast your hardest hitting one from 100% farther away. Only take this if you're not listening to me and building into one ability.

Level 16

Preferred: Northern Exposure
Okay, so if a 65% increase in damage to chilled targets wasn't enough damage for you, then how about an additional 25% vulnerability increase to targets hit by your Cone of Cold?! By taking this talent you can initiate fights with ( Cone of Cold) and then following up with Blizzard, while using Icy Veins to reduce the cooldowns dramatically, all the while spamming Frostbolt until your heart's content.

Optional: Numbing Blast
If you've found that your opponents are particularly slippery, then this talent could be useful to you. Being able to root an opponent can help, but isn't it more fun to just blow them up? With this talent I've also found that you have to use Blizzard to initiate (to apply chill), which will then allow you to root opponents with Cone of Cold. Maybe I'm just used to hitting E first instead of W, but it's much easier to hit a target with both waves of blizzard if the target is slowed first.

Optional/Avoid: Snow Crash
This is another upgrade to Blizzard. If you're building into it (for some dumb reason), then why not continue to buff it more, I guess. If your target is slowed, rooted, body-blocked, or whatever, you can usually land two waves of your Blizzard, but you probably won't be able to land three (they'll just walk out of the range). But hey, who knows, maybe someone won't be paying attention to your talent selections and stand in it for three waves.

Avoid: Ice Barrier
I'll be honest, I've never taken this talent. I mentioned already my stance on defensive picks for Jaina, and this one I have the same opinion on. Why take defense when you can just make them explode? If you've already picked all the defensive talents maybe you should pick this one too, otherwise don't bother.

Level 20

Preferred: Wintermute
This upgrade to your Summon Water Elemental is the scariest damage output you will ever see. Let's recap, if you've taken Deep Chill, Arcane Intellect, Frostbitten, Icy Veins, Northern Exposure, you will slow enemies by 35%, never run out of mana, increase your damage to chilled targets by 65%, have your ability cooldowns reduced by 3x, and increase your damage further by 25%. If all of that pure carnage wasn't enough, your Wintermute will now mimic your abilities for 50% of the damage. OH MY GOD. THE DAMAGE OUTPUT WILL MELT ANY HERO. But for real, if one cycle of your abilities isn't enough to burst down the tank you're facing, your next Frostbolt will be ready in 1 second, Cone of Cold in 3.3 seconds, and Blizzard in 5 seconds with Icy Veins active.

Optional: Bolt of the Storm
If you didn't take Improved Ice Block, and you're starting to realize you can't avoid getting blown up, then this talent is very useful. Sometimes you're in a game and you just can't seem to do anything but get blown up as soon as a team fight starts. It's okay, this talent can help alleviate some of the pain. And hey, maybe if the tide has started to turn in your favor, you can use this talent offensively to get in casting range to blow people up like you've always dreamed of.

Avoid: Arcane Power
If you've listened to anything I've said and have taken Arcane Intellect, mana shouldn't be a problem at this point. Increasing your ability power by 15% isn't even comparable to what your Wintermute can do either.

Avoid: Cold Snap
This talent fixes the problem of people going inside your Ring of Frost. However, Ring of Frost is still not that great of a talent, especially when compared to the power of Summon Water Elemental. All of the other level 20 talents are more viable than this one.

I know that this build is not for everybody, and that a lot of Jaina players rely on Improved Ice Block and Bolt of the Storm to survive. However, if you're looking to blow people up, and put up some ridiculous hero damage numbers, this might be the build for you. I've had decent success with it in both quick-match and hero league, with a win-rate of around 60%.

Here's a link to my hotslogs if you're interested in seeing how successful I've been with different Jaina talents: Reid's Hotslogs