Hold A on the item you want to move, use triggers/bumpers to navigate to where you want to put the item (ie backpack, shirt), then release A. If there is free space, it will move. Keep in mind that with some items the actual capacity varies from the listed capacity.
Can someone please elaborate on Brandon Thomas's above post and explain the weapon/magazine glitch in more detail? Every gun I have picked up so far has had this issue. Is it caused by navigating to the mag in the gun's inventory and removing, because that is what it seems like to me. If I reload by pressing Y, pressing RT to load a mag from the floor or combining the mag from the inventory it seems to work alright, but if I remove the mag myself it seems to think there is a still a mag inserted and shows it on the gun, although there is none. It makes keeping your gun and mags loaded a PITA, I really hope a patch fixes this soon.