IIRC mobs will only spawn within a certain radius of a player, but not spawn within a closer range...
So it might be (and I don't know the numbers, you'd have to google) that they will spawn at 20 blocks from a player, but only within a 100 block radius of that player...
So essentially you'd want to then be no more than 100 blocks away from your spawner, but no closer than 20 to it. (whatever the number is)
Some people's spawners use multiple levels with flowing water in a sort of + type configuration, channeling down into a hole in the centre. The idea being that the mobs will spawn on the non-water surfaces, fall/walk into the water and be pushed along, falling down the hole onto the layer below (or right down to the catchment area if you like). Doing that you can make a bigger spawner that has more surfaces for mobs to spawn on, increasing your loot.
Personally I've only ever made the other kind, where you take a mob spawner you find in the world and build a trap around those - I've used water channels around the dungeon room to take them into a water-elevator, then dropped them into a small hitting area - where you can 1 hit kill them with a bare hand, and you get loot and XP. (And since you're standing there punching them, you're getting all their drops and don't have to remember to come back for them)
With those I make an on/off switch by putting a torch recessed (or a glowstone block) in the ground on each side of the spawn cage (as in cage, spare block, recessed block) with a sticky piston wired up to cover the light-holes with the flick of a lever. So when the trap is "off" the piston is raised and the light from the torches lights up the spawner enough to stop it spawning anything. When the trap is "on" the pistons are lowered, covering the light blocks so the room goes dark and things spawn.
Bazz nearly killed our server once I recall.... he decided to go AFK in my mob trap to let the zombies collect a while so he had lots to kill.... and forgot to come back for a while..... So the server just about ground to a halt because there were TONS of zombies in the trap
So be careful about that!!