One of the cheapest ways to build a platform bed frame is by using cinder blocks. You won't have to buy expensive wood or metal or screws; you won't even need any tools, and because the materials can be so cheap, even if you have a king size bed, your total cost can be under $50.
Determine how many cinder blocks you will need based on the size of bed you have. For a twin bed you will need four blocks, for a double bed you will need five blocks, for a queen bed you will need nine blocks, and for a king bed you will need thirteen blocks.
Measure and cut your sheet of plywood so that it conforms to the size of your bed. You'll want to subtract one extra inch from the length and one extra inch from the width, however, to avoid banging your legs or feet on the side of the sheet of plywood after you've placed your mattress on top.
Place four cinder blocks on the floor so that they correspond to the four corners of your bed. Lay the blocks on their sides.
Place extra blocks on the floor if you have a mattress larger than a twin. Place one block in the middle of your configuration if you have a double, queen or king mattress. In addition, for a queen mattress put an extra block at the center of each side plus one in the centers at the head and foot, and for a king mattress arrange four extra blocks -- spaced evenly -- between the outer blocks and the center block of the queen sized format.
Lay your sheet of plywood on the blocks and re-arrange the configuration of the blocks if needed. Place your mattress on top of the sheet of plywood.