I have a question

You go to the people in the groups and ask to be let into the group.

Or wait for them to do an entry drive in the forums here.

for the private ones, any number of ways. Basically the person doing the giveaway does either a puzzle or something like that to tell you the link and you enter it like that.

This is a useful guide as it talks a bit about groups.

If you want to join a public group, you just need to go to the page for it and click Join. Private groups have different requirements, but generally, you will need to be active in the forums and in making giveaways before you get an invite to most. They don't tend to welcome people who just want to leech their giveaways without offering anything themselves, and so you need to prove yourself first.