High House, (Clay shooters pun)
Chokes really are very simple (Ha!), they are varying degrees of constriction at the end of the barrel which control the percentage of shot in the critical 'killing' area of your pattern at a given distance from the end of your barrel. There is no industry standard and different manufacturers use different constrictions for different chokes.
The most common designations of chokes is as follows:
Cylinder - there should be no constriction
Skeet - slight constriction only
Improved Cylinder - usually 1/4 of full constriction
Modified - usually 1/2 of full constriction
Improved Modified - usually 3/4 of full constriction
Full - Full Constriction
Extra Full - More constriction than Full
Another small spanner in the works is that every gun patterns every different cartridge type differently. Therefore, if you had two Remington 870's, they might need different types of ammo (not likely, but possible). These differences in pattern are usually not detectable to the shooter. The key is to find a cartridge that you are happy with. Follow Big Bunny's advice and check out what works well in your gun.
A major myth is that barrel length affects patterning at longer ranges. The difference between an 18in barrel and a 30in barrel is twelve inches. If they have the same choke, twelve inches is the only difference at any given range. Choke is key to effective shotgunning and if you have to err on the side of caution, go slightly tighter with your choke rather than more open.
For wildfowling, please use a full choke as clean kills are desirable. Please refrain from shooting at ranges over 45-50yds as you are more likely to wound your target than kill it.
For clays, you will seldom need anything tighter than improved modified (long sporting clay shots and ISSF Olympic Trench excepted) if you have a good patterning gun. Have Fun and try ISSF Skeet.