How do I cover a bench seat with fabric without it looking rumpled?

Use the removable seat as a template to cut the fabric. Be sure to leave at least 3 or 4 inches on all sides. Once your fabric is cut to fit, you can start at the center and staple the fabric to the bottom of the seat. I recommend using a staple gun for this project. Then turn it and pull the fabric and staple the center on the next side. Do this on all 4 sides. Once all four sides have a center staple, then go back and staple the rest of the fabric, pulling and stapling as you go. You can leave an inch or so between staples. After you have it all stapled, then you can cut the excess fabric off. You can get pretty close to the staples when you cut the excess fabric. I hope this helps you. Good luck.

Well you must use some cushioning, like foam and as thick as the seat will accommodate. When you lay your foam on the board (or seat) fasten it securely so when you flip it over it stays in place. Start by first stapling in the middle of a short side, do the opposite side also one staple in the middle, then the middles of the long sides. Then the ends all around, then back to the middles, in other words don't just start stapling in one continuous run, you have to space them out, pulling tautly for each staple you put in.

If the seat is square you can wrap the fabric like a present. Start by stapiling one side and pulling the opposite side and stapling, alternating from side to side. Then do the ends the same way. If it is round, make small little pleats on the underside as you staple the fabric in place to keep the fabric smooth and from bunching.

https://www.hometalk.com/diy/upcycle/old-vanity-bench-redo-1126009

Also make sure that you have a dense foam pad and cover it with batting like for a quilt you cover the foam with the batting to make sure that once you replacing the seat the batting should help so that you don't feel edges of seat then do exactly as the previous person said and you should end up with a beautifully finished product.

You want your fabric to be tight, but not to the point that the cushion curls. It could be that your fabric is too thin and gives a little too much thus stretching. If that is the problem you can sew a panel of neutral colored, heavier fabric to the backside of the top and bottom panels by stitching in the existing seam from the right side (stitching in the ditch).

Here is a little knowledge nugget for you: there are three directions on fabric, the length is the straight of grain, the width is the cross grain, and the diagonal is the bias. The bias will stretch and curve on woven fabric.

If you are going for a complete do-over lay your pattern (size and shape of cushion and batting plus seam allowance) so that the long edge is parallel to the salvege edge (the edge of fabric with information on it), this is called the straight of grain. If your fabric's print is obviously running from edge to edge then you need to square up your fabric's end and place your pattern so that the short end is parallel to the salvage. Home dec fabrics can be 60 inches wide, but if your cushion is longer than that you will need to sew three pieces of fabric together while matching the print. You would be looking to have two shorter pcs and a wider pc in the center. If that arrangement is making the two side psc too narrow then decrease the width of the center panel so that you have better proportions. It's a judgement call but you don't want to do it in two pcs with the seam in the middle.

If you are not comfortable with all of this piecing I would suggest that you choose a fabric that can be used long ways on the cushion, this is called railroading your fabric. If this is a box cushion and you plan to have cording in the seams I would suggest that you buy enough double fold bias binding in a matching or coording color and cover the cording using the zipper foot of your machine. You can make your own bias binding, but it requires that you cut strips of fabric on the bias and you may not be there yet in your skill set.

In all of this it is important that you work within your limits or you will not be happy with the outcome. If zippers and cording and pattern matching are not what you want to do, then just keep it simple. In the end, it is yours and every sewing project is a learning project. Keep plugging along we learn from our mistakes, experience is the best teacher.