You can build a slat bed frame from construction lumber, using a saw as simple as a human powered crosscut saw. I built one for about $50, because I was disgusted at the quality of the store bought frames.
Use 2x8 lumber for the sides, a 2x4 or 2x6 for the center support rail, 2x4 with a decorative slant cut for the feet. Get the bulk packs of 1x3 lumber for slats, they work well and space the slats apart using a 1x2 or 1x3. Use self tapping wood screws and a drill or even a screwdriver to put it together.
If you want it to look nicer when you are done, spend another $25 on sandpaper and stain/paint. This is a 2 night project if you are new to it. Add another 1-2 nights for doing optional finish work.
I vaguely followed this plan, but made some cost saving changes. I skipped the top rails and the finish. If you don't plan to do a headboard, make sure the feet will allow the bedframe to push up flush to a wall (baseboards can get in the way).
Spend money on good self drilling screws, it is worth the time savings. I like the ones that use a torx or square drive bit to drive them in. A drill is a big time saver. A power saw saves only a little time for this project vs a handsaw. I skipped the finish because my bedset has a skirt designed to cover the box spring. This style of bed does not use a box spring. The skirt covers the bedframe instead.
If you want storage underneath, make your feet the right height for your bins. I made my bed feet to put the mattress top at the same height as a kitchen chair, so my mother could get off the bed easily.
http://www.ana-white.com/2012/01/plans/hailey-platform-bedhttp://www.ana-white.com/2012/01/plans/hailey-platform-bed