So, here's the wonderful coffee table in all of its glory:

First I measured it, and then I went to the fabric store to get upholstery fabric and muslin that would cover all four sides and the top. The fabric is where this project can get pricy. I also got some 1/2 inch foam:

Here's my staple gun. It kills by hands but it does the job okay.

To get the tight/cushiony effect that I wanted, I spray glued the foam onto the table (after I cut it to the size of the top of the table (plus an inch or so). After that, I cut the muslin out so it could be pulled over the foam and stapled to the bottom of the table:


When I finally regained the will to DIY, I got out the fabric I bought months before and sewed it all up. The cover is pretty simple, just the sides sewn to the top and hemmed. I made ties for the corners so it looks more finished.
The cover is basically a table cloth that ties on the corners because I wanted to be able to remove it and put it in the washing machine. We have a dog, and his hairs get all over everything! Also, I'll be able to change the cover when I feel like it. I might get some modern looking fabric next time!

Overall, I don't think it looks perfect, and it doesn't really look like one of the cool, high end ottomans for sale but it's an improvement! Cheers!
