This is how I made a low-profile bed frame cheaply from wood slats.
We want our mattress low to the ground so if our daughter ever falls out of bed, she doesn't have far to go. We learned the trick of putting the family bed on the ground from Christy's parents, and wanted to give it a try. However, the floor in our bedroom is uninsulated, and putting a mattress directly against a cold floor is a great way to grow mold. This frame raises the mattress 1.5 inches; just enough to ensure airflow.
Step 1: Build the Framing with Furring Strips
My local Home Depot had 1x3 8 ft pine furring strips (0.75 inches x 2.5 inches actual) for $1.22 each. These things aren't particularly straight or high-quality, but they're perfect for my purpose. I bought 23 of them and a box of 1 1/4 inch nails for a total cost just under $30.
I measured my mattress, then cut all the furring strips to the proper length with a chop saw.