Yes, if you give her your wireless password (WPA key, that's called), she's using your connection and your data plan. So it's fair to share the costs. However, if it's a limited data plan, this can lead to problems (like she sharing the costs equal and the usage unequal, or she using up the whole plan in 10 days).
But just as well, your modem isn't wireless at all and then sharing won't work at all. If she connects her laptop wired to your modem/router, she doesn't need a password (wired access doesn't need a password), but still uses your data plan, with the same risk of the same troubles.
All in all I would advise sharing only if your data plan is unlimited. Otherwise, make it totally independent (although that isn't possible across a single telephone line only.
Kees
Hi,
I have a pc connected to the internet via a modem. A friend living with me has just bought a laptop and has asked me to give her my internet "password" to enable her to use the internet. Her laptop has a pre-paid plan and a usb card or wireless gadget. I thought internet access was standalone, i.e. it works like on a mobile phone anywhere close enough to a transmitting tower.
Does she need my password to access the internet? Will this mean she is feeding off my plan? I'm very green at all this and want to be careful.
I hope somebody can assist.
V. Green

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic