The computer doesn't have a limit :) You can't have more than one person using the same account, but you can create separate accounts. You'll need to login and out with the different accounts. Make sense? Let me know if you have more questions.
You can. Kind of a pain on a phone to log in and out though. One solution (on a computer) is to each use a different browser. On this computer, IE goes to my daughter's account, and Firefox goes to mine. It's more of a pain to have multiple accounts on a phone.
If you don't want to have more than one browser, I've also seen the suggestion of using different user accounts (settings, users) in Chrome, but I've never played with this feature, but it may be worth a try.