There are a number of things that make Tyrael unique as a tank, and it is important to keep these in mind when tanking on him. He isn’t really an all-in tank like Diablo, and he isn’t a front line anchor like Johanna. If anything, he is almost a support hero in that he is strongest when enabling his team and countering what the enemy team wants to do.
Here is my most common build when tanking on him. Do note, he does have other perfectly viable builds, and I will use other talents when playing him as a bruiser, but since you were asking about tanking and solo queue QM, I am focusing on the talents that are pretty much universally decent.
Level 1 - Justice for All. Use your W whenever your team, or even just one team mate, is about to take burst damage. Also note that your enhanced W does apply to minions as well as heroes. I will often use it when pushing with a minion wave to allow them to take an extra tower shot or two, so I don’t have to.
Level 4 - Stalwart Angel. This can also help while pushing, and it helps counter the armor shred from towers/forts/keeps and allows you to stay in there a bit longer, which is often all that is needed for your team to bring down a structure.
Level 7 - Swift Retribution. Smite (E) is your bread and butter as Tyrael, and this makes it incredibly potent as an engage or disengage, so you can save Q for the fancier things.
Level 10 - Sanctification. This is always a safe pick, just make sure you use it before the nastiness hits, as it is easy to interrupt. Don’t get me wrong, Judgment is incredibly powerful, and so much fun to use, but you should learn when and how to use Sanc.
Level 13 - Holy Ground. Again, we are focusing on tanking, and Holy Ground can be used as a peel, area denial, isolating a kill target, and more. It can take some practice, but it is an amazing tool for a main tank.
Level 16 - If you need more damage, you can go Burning Halo, but I generally prefer Horadric Reforging, especially when I take Holy Ground at 13.
Level 20 - Defense of the Angels. You can now completely ignore the armor shred mechanic and you can set up a push that can lead to a win.
Regarding his abilities and how to use them:
Q - El’Druin’s Might. This is your main CC, escape, protection (with the armor talent at 4), mobility, and scouting tool. If you see a suspicious bush, throw a Q into it. Worst case, you put it on CD. Best case, there are enemies lurking, and now they are slowed, you have armor, and you could potentially disrupt and split them up with Holy Ground. Do not use Q as you main engagement tool in a team fight, as you want to save it for the armor buff when your health starts to drop, as an escape, or as a gap closer/slow when they want to leave.
W - Righteousness. This should be used when you have multiple allies near you to get the most value out of your level 1, to shield people from burst damage, or to beef up a minion wave. DO NOT SPAM THIS ABILITY! You should always be using it strategically, as W spam is main reason people have mana issues on him.
E - Smite. Since I typically take the level 7 talent to enhance the move and attack speed bonus, I will use this as my engage tool, and to buff any aggressive assassins/bruisers on my team. Practice placing Smite in places where your allies are guaranteed to run through it. It is also incredibly powerful for getting your team out of trouble, too. Again, DO NOT SPAM THIS! Use it to get in, or get out.
When playing Tyrael, he is amazing for enabling aggressive heroes who may or may not have escapes on their own, and can benefit from the attack or movement speed. Qhira, Imperius, TB Varian, Illidan, and Artanis are some of his favorite melee buddies. He can also enable a dive comp like no other tank, so heroes like Tracer, Genji, or Calamity Ming do very well with him. My favorite healers are aggressive and in melee range, so Rehgod, Kharazim, and Uther can shine with a good Tyrael.
If you have specific questions about things like engaging, Sanc use, or the like, let me know!