I presume you have a Linksys wireless modem/router. If you haven`t already done so set up WEP or WPA Encryption otherwise the whole street will be using your bandwidth - hope you aren`t on a capped service!
Basically you set up her computer with a new connection (called "My Mate`s Connection" or something) to gain access to your router through your ISP details. The fact that they`re probably the same as hers is immaterial Your password remains secret because once entered in her machine you can only see blobs. Set her machine to remember the password. She can then access the internet and surf.
For e-mail she needs to set up a new connection in Outlook Express (or Outlook) and name it "My Mate`s Connection". She enters all her username and password details for her account and in the options selects the wireless connection you set up earlier. You must tick the box "Always connect to this account using this connection"
That`s the theory - let us know how you get on! If you are on a capped download limit you`d better come to some arrangement if you haven`t already done so! Two people surfing can be expensive if you exceed your allowance. If the previous negotiations break down at any point - Change the encryption password at any time to suspend the service.
And ask the bill payer in the household for permission!