A note about fabric selection
For a beautiful, long-lasting tea towel, you will want a fabric with a heavier hand than quilting cotton. I would recommend linen, twill, or canvas. For my tea towels, I'm using Linen Cotton Canvas from Spoonflower. I'm not just pimping Spoonflower because I have designs for sale there...there are a few reasons this works well. First, the Linen Cotton Canvas is a durable choice for tea towels. Second, while a standard fat quarter of fabric is about 18" x 22", fat quarters of this fabric are 18" x 27", which is a great size for a tea towel. Third, Spoonflower introduced a feature earlier this year where you can Fill-a-Yard of fabric with multiple designs, so one yard of fabric can yield 4 different tea towels! This saves you money, and allows you to make unique towels for everyone on your list.
Now to dive in!
If your fabric has any selvedge, trim that away before pressing.