There are really cheap boats available if you just want a cheap boat (decent inflatables and foldable kayaks can be as little as $200-$300). Building a boat though is an adventure all its own, and can be quite fun. Building a boat takes hours (sometimes even hundreds of hours) and the cost of materials can often match or exceed the cost of a cheap off the shelf boats.
Materials alone on a decent quality ply wood boat will run hundreds of dollars, if not more. The plans can run close to a hundred dollars, but some free plans also exist. Ply wood boats also often require a lot of tools that most people do not own, like dozens of clamps, palm sanders, and wood working knives that could cost hundreds of dollars in addition to the cost of materials. If you are not looking for a 50+ hour time investment and a learning curve, buying a decent quality off the shelf inflatable boat for a few hundred dollars might be a better investment. If you do decide to build a boat, they can be a lot of fun and a building material to explore using for an emergency boat is corregated plastic. It is starting to see use by some manufacturers of small boats and kayaks and is relatively inexpensive as far as materials go (cheaper and lighter than wood). There was a company at one point a while ago that was investigating making emergency folding boats out of corregated cardboard but they may never have successfully launched the product. The boats were supposed to fold in seconds and serve as an emergency escape craft in the event of a flood. We have been investigating getting ahold of one of these designs to include on our site, but it has been a process. You may be able to find suggestions for building a DIY boat with Corregated Plastics, but if you can't and would like to learn more, let me know and we will renew our efforts to secure or put together some corregated plastic boat designs.