One of my favourite uses of tripmines is to reach people behind cover. For example:

Player A can stick a mine on the wall on the left to hit B around the corner. Works a treat, and they never see it coming.

I'd also recommend preempting enemy movement, but not preempting it too much. Often if you drop a tripmine too early people will see it and play around it. Of course, throw it too late and they'll never even have to deal with it. Ideally you'll throw it just before someone runs into an area. Good map knowledge will help you a lot here.

I often use tripmines to cut off an avenue of retreat at the start of an engagement. If my opponent sees the mine then great. They know they're cornered, and they'll have to play with reduced options. If they don't, even better. I now have the option of damaging them and then pulling back myself, as more often than not they'll duck back into cover to regen (and set off the mine). In the worst case scenario I'll die and then pick up a postmortem. The short version: chuck 'em behind people.

Another neat trick is to use them defensively when being pressed from multiple angles. You can turn a losing situation into a huge play. If you've got multiple enemies pushing towards you through several doorways, mine one of them and attack through the other. You'll take both groups by surprise, with one unable to advance (until they shoot the mine off - which is fiddly and time consuming, and usually prompts people to reload before proceeding) and the other suddenly finding themselves on the defensive.

One of the coolest ways of using them is when running away. Chuck them straight ahead into a wall before you round a corner and that dirty shotgunner will run straight into it :P

Also, watch out for survivors. Lots of people are running very high armour builds which let them take a tripmine and survive, just (NB: sticking someone with a mine always kills them). Don't let all that damage go to waste. If you see 194 damage pop up and don't get a kill it could be worth pushing up. Those damage numbers are really really useful, too. Watch for them when the mine detonates. 194, 194, and 2 with one kill tells you there were three people there. One is dead (now respawning), one is almost dead, and one is almost untouched. From the radar you probably knew there were at least two enemies there, but now you know more. Use that knowledge to your advantage.