If you are familiar with simple construction it doesn't have to be a difficult project. Here is a video link to HGTV's simple easy platform bed. If you are new to DIY, I would also look into weekend classes, or see if there are any free seminars in some of the local hardware stores to get some practice or tips. Good luck!
Elinor....I have built a few "bed" platforms in most cases the plywood is over kill. I build the "deck" with 2 x4 and construct it a bit like the joists in a homes floor. With spacing at 12" or so the mattress or box spring will have enough support. By using the 2 x on edge like a floor joist they do not flex. A queen size would need 2 sheets of py...so that would add 45 to 50 bucks to the project.
I built a simple tallish version for our guest room king size. Here the legs are tall enough for use to use the space below for storing out camping gear in some rubbermaid "action packer" tubs.
Check out Ana White's blog. She has amazing tutorials as well as material checklists and blueprints.
I too was thinking Ana White while I was reading her question....what a GREAT bog!!!
My hubby and I have built them. It is tru the plywood is more expensive, but for a novice it is the easier way to go. Make the frame about 4 to 6 inches smaller than the matress and box spring and mount the plywood overlapping the the frame so that you have full support for the mattress and box spring, this will allow you the space for your feet when you are making your bed in the morning. Dont want to stub those toes.