I bought an old army backpack at a flea market for $5 and attached it to my bike rack.
I wanted it set up so that the bag could easily be removed and carried around as a backpack when I parked my bike.

I was inspired by this website:
http://web.archive.org/web/20041020064156/http://www.twowheelfetish.com/Ezine4/diypanniers.html
I was originally going to use the same method of making an internal dowel frame to keep the backpack rigid. But my backpack luckily had 8 metal rings on the sides that allowed me to attach it to an external frame and keep the backpack intact. No holes or sewing required, which is good, because I'm sure I would have screwed up the bag in some way.

My pack has "Bag Ammunition M2A1 034951" printed on it. Unless you've got the same type of backpack, you will probably have to attach it to your bike in some other way. Plenty of good advice here:
https://www.instructables.com/id/How_to_make_DIY_Bike_Panniers/?ALLSTEPS

Step 1: The Backpack

The Backpack has 4 little metal rings on each side, 2 near the front and 2 near the back. I am going to use these to hold the backpack up against a frame attached to the bike.

Step 2: The Frame

I got lucky with the frame because I happened to have a piece of aluminum lying around that could be bent to make a square that matched the size of the backpack exactly.

The aluminum was a vertical support from a screen door. It had four spots where it could easily be bent to form five even segments. With one side overlapping, it made a square with sides of about 14 inches. The backpack is also a square with 14 inch sides. How convenient.

Step 3: Strengthening the Frame

On the side of the square with the overlapping aluminum, I drilled three holes and used a pop rivet gun to attach them together.

This held the square together, but it needed more to keep the corners at 90 degree angles. I cut two corners off of a steel plate with a jigsaw to make two right triangles. I drilled holes through the steel triangles and opposite corners of aluminum, and pop riveted those together. Now the frame was much stiffer.

Step 4: Attaching the Frame to the Bike

Next I attached the frame to my bike rack. Since I could take the backpack on and off, I didn't really care how easy it was to get the frame off.

At this point, I spray painted the frame black to make it look way cooler on my black bike.

At the top of the rack, I used two hose clamps to hold it on.

At the bottom, I drilled a hole through the aluminum and used the same screw that goes through the bike rack and into the bike frame to hold it all together. The original screw was too short so I found a longer replacement.

Although the frame lined up nicely with the rack, I had to move it a couple inches further back on the bike because my foot would hit the backpack when pedaling. This just meant drilling a new hole on the bottom.

Step 5: Attaching the Backpack to the Frame

Originally I used a few bungee cords to strap the backpack on and it worked fine, but it was a pain to get on and off. I was considering using four little keychain carabiners to clip onto the backpack's metal rings on the but was having trouble getting them fastened to the frame.

Instead I found four little flat spring loaded clips that worked perfectly. They were attached to some unrelated straps I had lying around. I sawed them off and pop riveted them to the aluminum frame so that they were aligned with the four pairs of rings on the backpack.

Step 6: Done!

Now the pannier is complete. The backpack hangs on the four clips and shows no signs of breaking or falling off, even when filled with heavy stuff. The pack is held on pretty tight, almost too tight, since it's kind of hard to get the last ring clipped on or off and it can be tough to fit large objects into the bag. But it's better than the backpack flopping all over the place and it is possible to leave some of the outer rings unclipped in order to let the backpack expand and hold more.

Thanks for reading!