There are two ways to move your mail from another account to Gmail: forwarding mail and fetching mail. Both methods will transfer new mail to Gmail, but only fetching can transfer your existing mail. With either option, we suggest creating filters and labels in Gmail to help organize this mail.
Forwarding:
If your other webmail provider supports auto-forwarding, you can set your Gmail address as the forwarding target. This will only forward mail that arrives from now on.
You'll need to contact your other webmail provider to determine whether or not they support auto-forwarding, and for instructions on enabling it.
Fetching:
If your other webmail account offers POP3 access, you can configure Mail Fetcher in Gmail and automatically download all your other mail to Gmail. In a short amount of time, this will download all of your existing messages to Gmail, and will regularly check your other account for new mail.
You'll need to contact your other webmail provider to determine whether or not they support POP3 access, and for instructions on enabling it.