The boys have given good info, i love to fish the lift up rig as hammercarp has shown.
A regular slip bobber will work fine for carp, any float can be rigged right to work. I have used hair rigs with success under a float, but i prefer a regular size 8 or 6 mustad hook (i love the gold colour corn or roe bag hooks) with 2-3 kernals of canned corn directly on the hook.
Most of the time you want your bait to remain motionless on the bottom, so make sure you have a split shot or something (tungston putty rocks!) about 4-6" away from your bait holding on bottom. Have the float set as precise as you can so you can set the hook quick (and not loose a rod to a fatty!).
If they are confidently feeding on the drop, use split shot getting smaller as you get to the hook, to slowly sink your bait past them.
If they are on the surface google 'controller float rig' awesome with bread or dry dog food!
Fluorocarbon is your friend and will sink nicely and be invisible (ish) to hogs.
Float fishing is one of the most deadly techniques for carp, a little patience will heap gold rewards!! If you can see them, don't cast on their heads, but 6' in front of them, let them discover your bait on their own, chum little and often, especially in a river!
May you burn out the drag on your favorite reel!