There are wanted posters in various spots on the map. They are all magically linked through a wanted-poster-network. That is, if you're on poster #3, you'll see poster #3 all over the world, until you clear it and move on to #4.

#1 - George Whiskers Mahonee
$10 dead, $15 alive, known to be gambling in saloon.
You get an X target. Go on in. Your note says grab him, then hit the button to subdue him. Note that you can't just grab him uninjured. You have to "hit" him once (with your gun or knife) then you can grab and subdue.
Reward: +2 gunhand, +3 quickdraw, +4 melee, $15 cash

#2 - Butch Mainard
$10 dead $15 alive, shown on map
This unlocks once you get to Empire. You'll need to ride your horse out to his location. He's on a horse too. Trample him to get him off the horse. Then hit him a few times to weaken him, then grab him and subdue him.
Reward: +2 gunhand, +3 quickdraw, +4 melee, $15 cash

#3 - Johnny Greed
$10 dead, $15 alive, with friends
If you start this in Empire, you pass gold on the railroad track towards the X. There's a big patch of gold going straight along the ditch path in cave, so 3 total. If you keep going along the narrowing path, you hit a dead end. Go back past the 3-rock pile, under the circle arch and bridge. Go up across to the top of bridge area and right. There's gold over on the right after the arch that's freestanding on the left. You see Johnny Greed just ahead there, chase him down. The henchmen flee when you grab him.
Reward: +2 gunhand, +3 quickdraw, +4 melee, $15 cash

#4 - Shifty Shultz
$15 dead, $0 alive. They want the horse
You have to focus on keeping the horse alive here. You run into gold along the way, in a narrow rock passageway up from the grey bridge. When you kill him, his henchmen still attack, so you have to kill them too. Ride the horse back to the marked spot. He says thanks - he's going to turn it into glue???
Reward: +2 gunhand, +3 quickdraw, +4 melee, $15 cash

Gun Walkthrough