My third (ever) sewing machine project was a simple pillow case. I used a relatively heavy upholstery fabric and it only took less than half an hour.
I hemmed either short end of the fabric, and then folded them over each other to create the envelope back (inside-out). I pinned these in place and then stitched down each long end of the case. Then all you have to do is turn it back in the right way and stuff with a cushion pad.