Gazlowe is a very underplayed hero, with some unique talents. With this build you will be focusing primarily on towers and merc camps. Gazlowe's talents make him very strong against tower minion and merc damage, and he gets a nice bonus to damage against them at level 10. Also he is one of few characters that can solo a Boss, which this build will let you do efficiently starting at level 16.

He isn't the greatest in teamfights, but his turrets will add some splash damage and his bomb charges add some decent stuns and additional area control. He also has some pretty strong survivability and can soak a bit of damage while your teammates dish it out. Your main focus in teamfights will be to protect your DPS by attacking anyone who charges them and using your bomb charges to stun or force them to move out of position.

In general teamfights should be a low priority for you as Gazlowe, and instead focus on towers and camps.

Level 1:
I take Demolitionist. The damage bonus isn't anything special, but the ability to destroy ammunition is awesome. You can very quickly drain all the ammo from towers giving free shots to your minions and turrets.
Xtra TNT is also an option. I don't really use it, but it could give your bombs a bit more punch in teamfights, and take down minions even faster. For this build Demolitionist is the best choice.

Level 4:
Superiority is really the only choice here. It reduces damage you take from minions, towers, mercs, bosses, and even the core. This allows you to sustain an attack on a tower for much longer. At higher levels undefended towers will not even do noticeable damage to you. This is an must to make yourself a tower wrecking best. It is also a must for soling bosses. This talent combined with the others you choose will let you easily solo a boss at level 16 if you go in with full health and decent mana. Late game this combined with other talents will allow you to solo an undefended core. I have won games by doing a solo counter push to take down a core while the other team was focused on an all out attack.

Level 7:
Rockit Turret XL. This gives your turrets better splash damage in teamfights and helps mow down minions when tower pushing. This also helps you when laning, since without it minions tend to soak up the damage from your turrets instead of hitting enemy heroes. Engine Gunk is also solid, and could be used if your team lacks CCs.

Level 10:
Robo-Goblin is the only choice for this build. The point of this build is to go all out on tower and merc damage. Once you get this Siege Camps are a joke, and towers and keeps go down quick. This is the talent that really kicks this build into high gear. It is also vital for soling Bruisers and Bosses efficiently.

Level 13:
I use Turret Storage here. The extra turrets help with tower pushing by soaking damage and doing damage of their own. They are also great for maps where you need to hold down an area or objective. Also the extra turret will help when going solo against a boss.

Level 16:
Kwik Release Charge. Extra bombs are invaluable in team fights for CC and positioning. They are also your best tool for making an escape. Drop one along your retreat path to force your enemy to go around or get stunned while you run away. This also adds extra DPS when taking down towers and keeps helping you do major damage and get in and out quick.

Level 20:
Hardened Shield is my top pick here. This is great for pushing out that extra damage on a keep or the core when things turn sketchy. It also lets you be more of a tank in teamfights, or take down a boss with less than full health. Mecha-Lord is also an option if your team already has 2 warriors and you need to up your DPS against heroes.

1. Towers
Sieging vulnerable towers is your top priority. Whenever you see an undefended tower mount up, drop some turrets and start whacking away. If your team is coordinated, you can often snipe towers and keeps while other people are focusing on objectives. If the other team is down players that is a prime opportunity to work down their towers.

2. Camps /Boss
If your team is down a person or two and you aren't needed at an objective the best thing you can do is take camps. You can efficiently do Siege camps at about level 7, Bruisers at 10+, and Boss at 16. The other side of this is taking out any enemy mercs in your area. Gazlowe destroys minions and mercs, so you are the best person for taking them out.

3. Objectives
This can take priority over camps at times depending on the situation. IF the enemy has a Garden Terror, Golem or Dragon Knight you are one of the best characters for burning them down. Also you turrets are great for controlling areas on maps like Cursed Hollow, Dragon Shrine, Sky Temple, and Blackheart's Bay.

4. Lanes / Defense
Protect your towers from minions, mercs, and enemy pushes. Dropping a few turrets and throwing a bomb charge or two can do wonders to slow the enemy down enough for your team to come help.

5. Teamfights
When the opportunity arises you can be useful for turning the tide of battle with your turrets and tankiness. I don't go out of my way to help on teamfights, but when the opportunity arises showing up to help can make a difference. Your bomb charges are also very helpful to aid teammates in retreating.

So, this is how you wreck it with Gazlowe. When your team is up people, play super aggressive and take out them towers. When your team is down people focus more on camps and defense. Help in teamfights and objectives when there isn't something better you could be doing. Over the course of a match you should end up with 200,000-250,000 siege damage and have the enemy keeps in a pile of rubble.

Have fun, and give em the clamps!