Mar K out of Oklahoma City has some pretty good bed assembly and installation instructions at this link:
https://www.mar-k.com/instructions.aspx
Quick answers are the cross sills hold the wood floor up, but also provide the bolting to the frame. There should be some angle strips on each bedside and the first, narrow boards go under those. The rest lay out along the sills and bolt to the bed front, rear cross sill, and support sills. Hopefully, this photo of mine will help a bit as well.