I've got a futon with the heaviest freaking mattress ever. I also have several cats that like to shed, so the futon needs a cover that I can wash. I had a zip-on cover for it, but getting it off the crazy heavy mattress involved an hour long wrestling match that usually ended in sweat and bruises; getting it back on after washing was twice the trouble. I wanted something like those fitted sheets that go on your bed; those come off in all of 30 seconds. I also wanted the cover to fit closely, without any excess fabric or wrinkles. To that end, I patterned a cover that fitted the shape of the futon mattress, but was styled after a fitted bed sheet.

I made this cover using equipment available at TechShop Menlo Park. I'll walk you through how I made mine, but I'm going to be vague about measurements because I didn't take many. Most of this I patterned by draping the fabric over the futon and cutting to shape.

To make this, you'll need the following:

A piece of fabric large enough to cover the top edge, backrest, seat and front edge of your futon plus about 16" to go around the back
Enough additional fabric to cover the side portions of your futon, plus about 8" extra to go around the back.
1/2 inch elastic, about 10' worth(ish)
Matching thread
Scissors
Sewing Machine
Two giant safety pins

Step 1: Wash Your Fabric, Even If You Hate This Step

First off, wash your fabric. This is the part of sewing where many people's projects fail before they're even begun. Fabric shrinks the first time you wash it. The entire point of this cover is that it can be taken off and washed. If you fail to pre-wash your fabric before you start to sew, the first time you wash the finished cover the fabric will shrink and your seams will pucker. Your cover won't fit anymore and will look horrible; even worse, you'll have wasted all the time you spent working on it.

A couple of tips for washing your fabric-

Zig-zag stitch or serge the cut edges of your fabric so that it doesn't become a huge frayed mess in the wash. See photo above for an example.
Wash your fabric on the same settings you intend to wash your cover on. If you plan to dry your cover on high heat in the future, dry your fabric that way. Remember, you want to get all the shrinkage out of the way before you start sewing.
Cottons, linens and some other fabrics will permanently wrinkle if you dry them completely in the dryer. No amount of ironing will get dryer-set wrinkles out of these fabrics. Instead, take them out of the dryer while they're still somewhat damp (not wet; just damp) and immediately iron the snot out of them.

Go wash your fabric. I'll wait.

Step 2: Patterning

My cover is made up of one main piece that starts at the upper back of the futon, comes over the top edge, then continues down the backrest and seat, around the bottom front edge and back underneath the bottom edge. Two shaped pieces with mitered corners cover one side and extend around the back, with a mirrored copy of those two covering the other side. The excess fabric that extends to the back is then gathered up with elastic to tightly fit and grip the mattress.

To get the main piece, I draped my fabric over the futon, arranged it as described above and cut it to size. The really important part is to make sure you have about 16" extra to wrap around the back. My fabric wasn't quiiiiiiiiite big enough though, so I added an extra strip + a bit of scrap along the bottom edge to make it the proper size. Take a look at the drawing with blue lines showing a side section of how I draped the blue fabric. Note the extra fabric trailing off the top and bottom.

For the side, cut two pieces approximating the red shapes in the drawing above. Note that I've rounded the edges a bit to better fit the mattress. As with the first piece, you want extra fabric that you can later pull around the back, so add at least 8" more than the thickness of the mattress. Make sure that when you cut the other side that the pieces are mirrored. You don't want to end up with two left sides, do you? Also, it doesn't show in the drawing, but the bottom part of my side piece was longer that the top one. Mark your pieces so you don't get confused about which is which.

A note on seam allowance- usually you'd add extra fabric to account for seam allowance, but I want this to fit really closely so I'm cutting my pieces to the exact size. It will end up a little tight on the mattress, which will hopefully eliminate any sag or bagginess.

You may want to zig-zag or serge around the edges of all your pieces now. This will ensure that you can wash the cover without the seams fraying. I forgot this step, so I'll have to go do it later.

Step 3: Sew the Side Pieces

Now you want to sew the mitered corners of your sides together. Be careful though; you don't want to sew two left sides by accident! Be aware of which pieces are tops and which are bottoms, and which goes to which side. I laid my bottom parts right side up and side by side so I could make sure they were properly mirrored, then laid the bottom parts wrong side down over their corresponding tops (see photos above). Only then did I commit to sewing them! The last image above shows the complete side pieces laying across each other so that I could fit them both in the image.

Step 4: Attach Sides to Middle

When I draped the main piece of fabric over the futon, I marked where the crease in the seat was on both edges. To sew one side piece to the main piece, I put them right sides together and lined up the inner corner of the side to the crease mark. I sewed them together from that mid point all the way along the inner edge of the side piece, then around the curved corner and down to the bottom edge. I then started back at the midpoint and did the same up to the top edge. I repeated the process with the other side piece.

Two things that helped with this process- I opened up about 1/2" of the seam at the inner corner of the side pieces so that it was easier to sew flat to the main piece. Also, when stitching the main piece around the curves at the ends of the side pieces, I made 1/2" cuts along the flat edge to better fit the fabric around the curve.

Step 5: Sew Casing, Gather With Elastic

Before you begin sewing the casing for the elastic, you'll want to stitch down all the seam allowances within 3 inches of the edge. If you don't, when you're trying to slide the elastic through the casing it will get hung up under one of the seam allowances and you'll never budge it. I zig-zagged mine down for extra security.

Once that's out of the way, fold over the edge about 1" all the way around. Stitch the edge down all the way around your cover, leaving a 2" gap open for you to insert the elastic. This part is going to be behind the futon, so it doesn't have to be pretty; if you want to make it perfect, you'll probably want to run a gathering stitch around the corners to ease the folded part down flat. I don't care about making this part pretty, so I just smooshed the extra fabric down with my fingers and sewed.

Roughly measure the edge of your cover and cut your elastic several feet smaller that that measurement. Pin one end of your elastic to the cover right next to the opening you left. Put the other safety pin on the opposite end of the elastic and insert it into the opening. Use the pin to push the elastic through the casing. The fabric will begin to gather up along the edge. You'll have to pause periodically to redistribute the gathers. When you get the elastic all the way around, securely tie the two ends together and let them slip into the casing. Try the finished cover on the futon to see if you need to shorten the elastic. If so, fish the tied ends out, cut the elastic shorter and retie the ends.