Here's a simple but effective bottom fishing rig made from common items found in most tackle boxes. All you need is a swivel, an egg sinker, a hook and about two feet of monofilament line for the leader.
Leader line, Crane swivel, Egg Sinker, and Circle Hook
First tie the swivel to one end of the monofilament leader (palomar, trilene, or improved clinch knots are recommended). Second slip the egg sinker onto the fishing reel's line then tie the reel's line to the other end of the swivel. Finally, tie the hook onto the end of the leader and you're ready to fish.
Completed Bottom Fishing Rig
An egg sinker permits live bait or the fish to take free spooning line without lifting the sinker off the bottom. However, a regular crimp-on sinker will work if no egg sinkers are handy. Use the smallest sinker possible, just be sure it is heavy enough to keep the bait on the bottom.
In most cases any monofilament line around 20 pound strength or more, should work as a leader when using 1/0 to 5/0 hook and this should handle most average fish. Circle hooks are highly recommended because a circle hook can set itself even on a slack line. Additionally, a circle hook will regularly set in the fish jaw before the hook can be swallowed which increases the survival rate of those fish released.
One more note about leaders, most prefabricated leaders sold in any tackle store that are plastic coated wire with swivel and designed for a single hook also work well for bottom fishing.
What type of fish could you catch? If fishing in brackish to salty waters expect croakers, redfish, black drum, and flounder. From brackish to a more freshwater also expect bass, stripers, and catfish, in other words "anything".
As for bait, live shrimp, finger mullet, shiners, or mud minnows, even baby croakers work.