Prior to posting the image to your the Facebook home page, and prior to posting on your timeline, you need may need to crop the photo in order for the entire pic to be visible (and not cut-off or partial-ized). Try the following image sizes for yout images (in pixels):
■ Facebook Profile Cover Photo: 851 wide x 315 tall
■ Profile Picture Size: 160 wide x 160 tall (or up to 180 x 180 to upload)
■ Facebook Timeline Image Post: 480 wide x 380 tall

In order to edit your photo you will need an image editing software program.
Some popular image editors are: Adobe Photoshop, Gimp, Microsoft Paint, Pixlr, Splashup, Inkscape, Seashore, Pixia, Photo Pos Pro, Picasa, and Photo Plus.