Depends on how tame the bird is. If it's a nasty rooster I don't know, a sour old guinea, or something like a ring-necked pheasant, especially a mature male with potentially dangerous spurs, I play it safe and use my 'working' grip. I use my left hand to firmly hold the bird's feet, always being careful to keep a finger or two in between their legs to prevent them from rubbing painfully together or any spurs from cutting them. The bird's body can then be held draped over your left forearm, its head facing your left elbow and probably lying against your upper arm, and its left wing snugged against your body while your right hand (which for me is my dominant hand) remains free to tend to any initial flapping from the right wing or take care of anything that needs to be done to the bird's face, feet, etc. I find that even semi-wild birds will normally only try once to escape an immobilizing grip like this, and will then relax when they realize it's hopeless to struggle, at which point you can sit with them semi-lying in your lap should you want to do something with them like oiling their legs or trimming claws, spurs, etc. Just keep hold of their legs and they'll stay quiet.
For tame birds, I just initially lift them up with both hands, facing away from me, slip my right hand past their right side and under to support their weight by their breast as much as possible...hold them tucked against my chest. This is for birds that go limp as soon as they're picked up and let their legs dangle. In this case it's my dominant hand holding them and my left hand that remains free, and that's fine because birds like this don't struggle or really need to be restrained.
BOOM!
