After you have connected, and perhaps verified the server's host key, you will be asked to log in, probably using a username and a password. Your system administrator should have provided you with these. Enter the username and the password, and the server should grant you access and begin your session. If you have mistyped your password, most servers will give you several chances to get it right.
If you are using SSH, be careful not to type your username wrongly, because you will not have a chance to correct it after you press Return. This is an unfortunate feature of the SSH protocol: it does not allow you to make two login attempts using different usernames. If you type your username wrongly, you must close PuTTY and start again.
If your password is refused but you are sure you have typed it correctly, check that Caps Lock is not enabled. Many login servers, particularly Unix computers, treat upper case and lower case as different when checking your password; so if Caps Lock is on, your password will probably be refused.