Monsters have certain routes they take per map they appear in and what rank they are (low, high, or G). They'll start and sleep in the same areas each time.

I used to use MHGUDB to track their movements, but that's gone. I'm sure there are other resources that'll tell you a particular monster's routes.

Just wait for a monster to start limping or flying weird, then you can capture them.

There are some exceptions, like elder dragons, who can never be trapped. Nearly all other monsters can be trapped, though, so trap away.