Notes for DPS Build
So on the DPS build there is not much secret. Your basic combo will be Ult>E>Q>Blood for Blood. If you find yourself getting in 1v1 often, I'd suggest getting for tier 3 Searing Attacks. This will maximize your ult enemy erasing hability. so in that case, just Ult>Searing Attacks>E>Q>Blood for Blood. If target is not a tank nor being healed, a kill is guaranteed in most cases.
BTW, You can pick Searing Attacks for tier 3 if you find it works better for you (I do it quite often for burst damage).

Notes for Full Tank
So on this build, on tier 1 you get Regeneration Master along with Amplified Healing on tier 2, and Angelic Absorption on tier 5. That means you have to collect as much orbs as possible, so when shielded, you'll get insane regen. If being healed, GG. On tier 6 you can pick Blood for Blood too if you just want that active "heal" (lifesteal in fact).

Notes for Tank and DPS
Now let's be honest. Tyrael is tanky enough without its talents. Now this build is not a true tanker, so for Tier 1 you can actually get Purge Evil if you just need the damage. What you do with this build is, maximize your shield for DPS usage. So it explodes for damage and slows enemies (Both attack and movement), meaning that you have to shield often, meaning you'll be tankier. Tier 7 Hardened Shield just for the extra tankiness. If your team is stomping, just go for ult upgrade or Nexus' Blades.

Notes for Tank and Support
Now for this build, I decided to get Sanctification for your ultimate. Have in mind that, this build only works if you have another tank in your team, so you're going support. Basically it maximizes your shield duration and strength, + gives you that slow on movement and attack speed when enemies attack you while shielded, to help your team mates. Ult upgrade to help your team deal most damage.

Most effective builds
Now being all honest here, the last two builds are only built by me when nescessary. Honestly the Tank and DPS is quite rare, but sometimes I end doing it. The most effective are hands down the DPS, then the Tank. People often overlook Tyrael's damage capabilities, but as explained in my DPS section, its ult combo is devastating. If focused on a healer and team follows, target may even die before you Q him, saving up your Q to follow up attacking with Searing Attacks if speced, and even slow/damage with Blood for Blood. IMO, Tyrael is Tier 1 if played correctly, so I hope this guide helps you getting the most out of this champ. Always remember, that you may have to change this and that talent to better suit the match and composition you're facing.

Have fun GG