I should warn you before you read further: I have had two sewing lessons in my life, one from my Aunt Karen and one from my fab friend Sara. Both lessons were on envelope-back pillows. Any other sewing performed on this site is self-taught. If you are a seamstress I will make you cringe.
Next, I measured the ends, sides, and bottom of the inside-out basket liner. Modification for a basket with no liner is to measure the sides of the basket and the basket's base to get your dimensions. Remember to add extra inches to the height of the side panels to account for a fold over the sides of the basket. Also, add a 1/2 inch to the width of each side panel for the 1/4" corner seams. For example, if your basket sides are 10 inches long, cut the fabric 10 1/2 inches long and make 1/4" seams along the corners. I planned to make a hem along the top of the folded over side panels, like the one seen in the photo, so I added 1/2 inch to the height of the side pieces. The bottom should be as precise as possible for a good fit down in the bottom of the basket.