You stick either a landing net (Copper River) or a dip net (Kenai area) in the water and wait for the spawning salmon to enter your net. Once you feel them hit the net, bring it in, cut a gil, and put the net back in. Oh yeah, dont forget to mark your Personal Use Permit and clip the tail fins!
Different tactics are used, some stand on shore, some float in a boat, some wade out in chest deep water to get to the fish. Ha, some even tie off to trees/rocks to hang down near the water to get the "good ones"!