Most sheets have a nice wide top hem. If you open the edges with a seam ripper, the rod will slide right in.
I agree with Laura. Also, if you want a bit of a ruffle to stick up above the rod, after you've opened the seam, sew a line of stitching across the sheet about an inch and a half below the top. Then insert the rod in the pocket made by that line of stitching and the stitching that "hems" the top. (If using a wide rod be sure it will fit before doing that extra line of stitching.)
If you want the curtain to have the wide hem at the bottom and the sheet is long enough, you can reverse the sheet and fold down, and sew two lines to make the pocket (or one line if you don't want the tiny ruffle sticking up). Because the edges are already finished, you can just fold down and sew without having to do any extra folds under.
For a completely no-sew instant curtain, use clip rings to hang the sheet from the rod. "Puddle" the bottom if too long.
Great additional details, Lizbeth! 👍
Here's a no-sew tutorial: https://www.youtube.com/watch?v=kYN1qXH0LNA
Skip all the fiddling. Use curtain clips! I have them in 2 rooms (so far) and I love them!