I see you got a great answer - I have never done a tissue box - but I did do a box or tall basket and followed the same proceedure as stated here. Good luck - can't wait to view this in projects. *4U
It is easier to zigzag the pieces together before you rinse them out if it is FSL. After you rinse them out they get very stiff.
Use a zigzag to stitch them together starting with stitching the top piece to each side piece all the way around.
Then zigzag the sides together starting at the top and easing the sides together till your to the bottom.
I always back stitch at the top before starting down the side and back stitch at the bottom to secure it from coming apart. Hope this helps you.
This is the pattern I'm stitching out, if any of you have it. How to attach the sides??