I ordered 2 sheets of king sized sheets online and gave it a go! A friend of ours orders microfiber sheets from Wal-Mart (I know, I hate them too, but these are great sheets) and they are so comfy, very lightweight, dry in just a few minutes on the line, and are only $20. Check them out here if you're interested.
The flat sheet is easy. I just draped the sheet over the mattress and the got under it and rolled around a bit to see how much sheet we really needed (this is a very technical approach obviously).
I decided to leave about 12" on either side and then cut the sheet to the shape of the mattress and hemmed it all around. Done! Now there's not a ton of fabric to get all tangled up by your feet!
The fitted sheet takes a bit more work. The sheet fits perfectly on the top corners of our mattress so all I had to do was make the bottom fit. I decided that I would fold up the bottom to make it like a pocket that fits around the bottom of the mattress. That way you can just slide the pocket over the mattress when you make the bed and it stays put.
I put the sheet on inside-out so after I trimmed the sheet to size, I could pin it all up for sewing.
Here's the bottom sewn up. I pictured the sheet like an envelope and you can see that's exactly how I sewed it together. It's easier for me if I have a visual in mind - maybe that'll help you too. From this point, I sewed the middle together up aways to make the pocket deeper and to make everything fit as nice as I could.
And here's the finished product - not too bad for the first set! The second set I made turned out better, but I didn't get any pictures.