Measure circumfrence of basket, add 3 or 4 inches. Cut a piece of fabric the length and width of the circumfrence and height of basket.
Iron under the width or the short side of the fabric.
Start hot gluing the fabric. Glue the ironed edge first. Glue it with the right side in the basket, so that you are looking at the wrong side of the fabric.
Keep gluing around the basket. The top edge can be a raw edge.
After you are done gluing, flip fabric inside the basket.
The edges will overlap. You can secure them with hot glue and secure the fabric in a few places in the bottom of the basket with hot glue.
Trace around the bottom of the basket on a piece of cardboard (if you shop at Costco you will have a plethora of cardboard).