Visit lumber yards, liquidators and home improvement centers and ask if they have any discounted lumber. Sometimes wood used for fencing has flaws that won't affect its use but because paying customers prefer unblemished pieces, the wood ends up in a discount bin.
Check Craigslist and your local paper often to see if anyone is replacing present fencing with new fencing. In such cases, you can get metal, vinyl or other fencing materials for next to nothing as long as you can supply the labor.
Call nonprofit and second-hand stores to see if they have any donated fencing on hand. Habitat for Humanity (habitat.org), for instance, stocks a large amount of building and home improvement materials. You may not find enough fencing to do your entire yard, but if you are using common fencing supplies like chain link, you can pick up much of what you need for a fraction of the cost. When you purchase your supplies at a nonprofit home center, the money you use to purchase your supplies helps those in need.
Ask your immediate neighbors to pitch in. If your new fence is going to benefit your neighbors, ask if they are willing to contribute half the cost and labor for the portion that borders their property.
Consider building a partial fence, if the need is due to privacy issues. As long as your neighbors aren't higher than you are, a 6-foot high partial section of fence will give you and your family privacy without costing a fortune.
Visit a home improvement center for temporary fencing supplies or if the fence is to protect your garden from wild animals. Not only do most home centers stock inexpensive chicken wire and netting, but most have experts on hand that can tell you what you will need and how to complete your project.