You can make cheap backpacks, but I don't think you should. Unless you are very good at sewing, it probably won't turn out the way you want. Also, even if you are an expert, it might take you less time to work an extra day and buy a pack with the money you make.
On the other hand, you can make a cheap backpack out of an old backpack frame. Take off the old pack and tie a plain nylon duffel bag with the zipper facing out to it in a tight knot. Small bungee cords can be used to connect it. I did this with an old aluminium frame that still had straps and a waist belt. For the price of a $15 duffel bag, I had a backpack with an external frame that could carry a lot and only weighed two pounds.
Getting cheap backpacks is a good idea.
You can get cheap backpacks in a few different ways. The easiest thing to do is just to wait for a good sale. Shopping online for a used pack is a faster way to get one. Try Ebay.com or go to whiteblaze.net, which is a forum for backpacking and other outdoor activities where people can sell their gear. You can easily ask questions about the pack on the forums, which is a nice feature.
You can also find cheap used backpacks at yard sales. Keep an eye out for outdoor gear in the ads and give them a call to see if they have a backpack you might want. It's possible that you could buy it before the sale starts. If not, start shopping early and try to get a good deal. At a garage sale I just had, I sold a beautiful Kelty frame-pack for $15.
There are sometimes cheap backpacks at thrift stores. Most of the time, they have day packs, but sometimes they don't. I've seen big, worn-out frame packs at thrift stores, and it occurred to me that for a few dollars I could just throw away the pack and use the frame with a duffel bag, as described above.
Going light is another way to save money. The small packs are always cheaper than the big ones, which is different from other small items. If you've been thinking about getting rid of some things, you can also save money. Most ultralight backpacks weigh less than two pounds and don't have a frame. Most likely, you'll use a sleeping pad as a sort of "frame." The good news is that you can often buy them for less than $100.
Go-Lite has a few packs that cost close to $100 and are sometimes on sale for less. The Granite Gear Virga Ultra Light Packer may still have a list price of less than $100, and I have seen it on sale for less than $80. It also only weighs 21 ounces, which is a plus for me because I like cheap and light backpacks.
