What You Need
Oversized T-Shirt (mine was fluorescent yellow)
Another T-Shirt(s) (to cut up for the straps)
Sewing Machine or Needle & Thread
Scissors & Sewing Pins
How To Do It
Lay your oversized t-shirt flat. Fold in half lengthwise so that armholes match up.
Cut off the sleeves, making sure to follow the curves and remove seams. Remove the neck, cutting straight across just below the lowest point of the collar.
Open the t-shirt back up and lay flat. Fold the top inch of the new neckline down on the inside and pin. Sew along this line. You can finish the hem nicely, but...eh, it's summer. This makes a channel for your strap.
Cut strips of your other t-shirt (I used 2 - blue and pink) about an inch wide (it's easier to fold it a bunch and then cut). This will give you loops so cut the loops to make a strip. Tie the ends of your strips together to form longer strips. The goal is 3 strips about 4 feet long. When you have that, tie the ends of your 3 strips together and braid them. It helps to pin them down and work slowly to avoid tangling.
Thread the braided strap through one of the channels you created at the neckline, looping through both in a "U" shape and ending with 2 loose strap ends on the same side.
Turn the t-shirt sideways so that the armpit is over your chest and the loose strap ends are in front. Tie the straps behind your neck and TA-DA - coverup! You can also wear it the "right" way and just tie the straps over one shoulder.
I added a pink ruffle to mine afterward because everything is improved by a pink ruffle. I hope this is clear but I would be happy to clarify or answer any questions that you have!