Hamster shows have two parts: main classes and pet classes. The pet classes are the best place to start as they are judged on tameness and condition, plus you only have to be there for part of the day not the whole show, and you can enter on the day and use your own carrier. For the main classes you have to enter in advance and be there for all of the show. You need to hire a show pen for your hamster as well.
The classes for each show vary between clubs and are on the show schedule. Show schedules for all shows can be found on the N
ational Hamster Council website. If you enter pet class, you just enter the one class that is relevant per hamster, ie male pet syrian, or pet dwarf.
Your hamster needs to be tame and healthy to enter in any part of the show, but doesn't need to have a pedigree, even for main classes. Hamsters that have been specifically bred for showing usually do better than ones which have not. Hybrid 'Russians' aren't permitted to be shown in the main classes.
You don't have to be a club member to enter. There are classes in the main show which you can only enter if you are a member, such as members points class and novice/intermediate, but not for pets. Many pet class entrants are members of the public who have seen the advertising near the halls and who aren't club members
I've written this from the point of view of shows held in England and Wales by NHC-affiliated clubs. Shows held elsewhere may be different.