Need something like Photoshop (but free).

I have a picture (jpg) of me and a female "friend", I like looking at her in the picture, but not at me.
So I'm looking for a program where I can cut me out of the picture (jpg)?

 

Picasa is free and easy to use. You can download it here on Major Geeks http://www.majorgeeks.com/files/details/picasa_photo_organizer.html

 

You can use Paint to crop the picture to include only your lady friend.
http://www.wikihow.com/Crop-an-Image-with-Microsoft-Paint

However, if you would like to try more advanced effects and editing, the aforementioned Gimp is a good choice.

 

If it's only one picture you need to fix up, you can download the 30-day trial for Photoshop.

Photoshop has that remarkable feature 'Content-aware Fill', which lets you select an unwanted object (using the quick-select tool), then fill the selected area to completely blend into the existing background.

See some examples at http://www.photoshopessentials.com/photo-editing/content-aware-fill-cs5/