Alright here's how you do it.
If your AD is weak early you'll want stun first and heal second. Then you max shatter or switch off between heal and shatter if your AD really needs it.
If your AD is strong early you'll want stun first and shatter second. And max shatter getting heal at level 4.
Play passive at level 1 in general unless your AD is strong level 1 like Draven. At level 2 with stun and shatter, you want to watch the health of your own creeps. Especially the caster ones because they are farther back. When the enemy AD goes to last hit a caster minion, he has to walk forward more and this is when you step out of the brush and try to stun and shatter him. This makes the enemy AD decide between last hitting a creep and taking a stun shatter + damage from your AD carry or backing off and missing the creep. If he backs off, do not chase for the stun. Even though you are Taric, you don't want to take free minion aggro. Your stun is for zoning and punishing positioning mistakes 90% of the time and maybe initiating a fight aggressively 10% of the time.
When you've stun shatter combo'd you generally want to back off unless the enemy AD is really really low. Chasing too far after chunking an enemy is the #1 mistake i see low elo players make. At this point all you can do is autoattack and take free damage. Just wait for your cooldowns to come up again and you can zone them even harder.
Do not waste your stun on the enemy support unless there's a really good reason. Because when your stun is down, the enemy AD will know he can play very aggressive against you. Do not waste your stun in general. If you stun the enemy AD and your AD is too far to follow up with damage, you have wasted it and now they can bully you until the stun CD comes up again.
Your burst is best at level 6 if you can get a stun, shatter and then ult on the enemy AD. This pairs well with a burst AD carry like MF. You may be able to hard engage 2v2 in certain situations at 6 but always know where the enemy jungler is before you do this or you could end up getting 3v2'd and double killed. Keep track of summoner spells and AD carry items. If your AD is sitting on 1500 gold and their AD came back from buying a BF sword, please don't initiate. If your exhaust is down and theirs isn't please don't initiate. Try not to flash stun unless you are certain the kills will be quick and/or the trade will be worth it. Otherwise you may find yourself without an escape and dying after an engage.