Bad photo - I know, but good enough for you to get the idea :)
Cut a band of stretch fabric (t-shirting etc) about 25 - 30cm wide. Measure the diameter of your waist, add 2cms for your seam & cut the band this length.
USE a stretch / ballpoint needle to sew the band into a ring (place right sides together & join with a stretch stitch).
Then fold both unfinished edges under 1,5cm, pin in place & stitch down, again using a stretch stitch.
I used my overlocker (serger) to do this - a normal overlock stitch to make the band into a ring, and a cover stitch for both edges. But you can use any stretch stitch on your sewing machine.
And there you have it! A simple solution to lengthen a shirt!
I bought this stretch at Volksfaden - they have a nice range of stretch fabrics right now, patterns, hearts, dots... go have a look!
Add elastic to the top seam! Most of us - even me who is pretty much straight up & down - are narrower in the waist than hips. So to prevent you pulling up your tube all day - add elastic under the fold over at the top seam & before stitching it in, test the tightness & then sew down. It will stay in place really well now.