Quote - I always have trouble with that too.  It seems more trouble than it's worth.
Even when I can get the picture to show up in the render, often times
it doesn't match the dimensions of the render and I get a white border
on the sides or top and bottom.

The borders are easy to get rid of. Just make sure your document window size (your workspace) is in direct proportion to your render dimensions and your background image. The borders appear when you use a 1600x1200 image as a background for a piece set to render at 1600x1280 for example.
My standard setup uses a workspace of 800x640, Render dimensions will be 1600x1280 or 3200x2560. So long as its a direct multiple of my workspace. Any background image I import needs to be in the same proportions. So a 1600x1280 background. (Or larger. 2400x1920 for example.) Anything else will produce unrendered borders.
Other than that just remember to select 'Render over Background Image' instead of over background colour in Render Settings and you should be good to go.

Expert in computer code including, but not limited to, BTW; IIRC; IMHO; LMAO; BRB; OIC; ROFL; TTYL. Black belt in Google-fu.