capturing

Wait till they are close to death, they will usually act differently, like some will have smoke come out of their mouths and others will jump up and fly away. Go find them and place the trap (it is a net added to a trap thing) and get him on it and put him to sleep.

They need to be weakened enough to be captured. This will usually be indicated in some way, Cephadrome and Plesioth will have their back fin down instead of up. Kut-Ku will have it's ears down. Gypceros and Garuga (although you will never be asked to capture Garuga it's nice to know when he's close to his demise,) will enter frenzy mode more frequently, usually after only a couple of hits (Gypceros especially, he once entered frenzy mode after just getting hit by a velociprey leap attack). Most of them will limp when hurt, maybe not to go to a different area but to walk to you (like Monoblos, Diablos, Gravios, Rathian and Rathalos). Some will try to get to a specific nesting area to heal when hurt, follow them to this area and lay a trap as they go to sleep and wake them up. They should fall into it, tranq them and BOOM! 'Target Monster Captured!'