Member authentification logic, need help

[Philopoemen]

Hi there,

I have a self-made 'forum' on one of my sites.
The problem is that for half of the users the authentification module doesn't work properly, something wrong with the cookies/sessions.

So I was wondering, can someone describe the logic of an authentification module here?

I DON'T NEED A FULL SCRIPT. I need only a list of steps, something like:
1. Take login+pass from a form.
2. Run query to MySQL and check for [this]
3. Do [that]
4. Save [here]
...
99. Drink beer :)

I appreciate your attention and help :)

[decepti0n]

0. Check if session variable exists, if it does, then ignore the rest
1. Login/pass form
2. Check if username exists, if not, return
3. If username does exist, fetch password
4. If password matches what they entered, redirect, set a session variable
5. If not, redirect back and tell them they got it wrong
99. Drink beer

[Philopoemen]

Oh, I forgot to mention.
I need the "remember me" function, so some members have to be permanently logged in.