Depending on the size bed you make, I added a couple more slats than are in the pic to hold the mattress. My dog likes to dig a "hole" in his bed so it needed support .
I used 1 x 10, 1 x 12 and 1 x 8 for the rails. You can use what you think to make the dog feel secure. These are just pushed in and are not attached. That way if you decide to put the bed in a different position you can rearrange the rails. My dog gets up on my bed and goes over to his bed. I don't need any stairs for mine. The legs need to be removable on this size bed so you can get it in the room. So just use screws, no glue or nails.
Please read through the entire plan and all comments before beginning this project. It is also advisable to review the Getting Started Section. Take all necessary precautions to build safely and smartly. Work on a clean level surface, free of imperfections or debris. Always use straight boards. Check for square after each step. Always predrill holes before attaching with screws. Use glue with finish nails for a stronger hold. Wipe excess glue off bare wood for stained projects, as dried glue will not take stain. Be safe, have fun, and ask for help if you need it. Good luck!