The cost of adding a fence around your yard or garden depends on two main factors: the size of the property and the type of fence you want to build. You can't really change the size of the area you want to fence in, so if you're interested in saving as much money as possible, go for cheap fencing. Remember, though, sometimes you end up paying more in the long run, as you may need to replace cheap fencing more often.
One of the most inexpensive types of fence is the chain link fence. You only pay $6 to $9 per foot (in 2010) for this kind of fencing material if you build a 4-foot-high fence, but the downside is that chain link fences aren't as aesthetically pleasing. They are typically durable though, so along with being cheap initially, they're inexpensive in the long run.
Found-material fences have a rustic look. Attain the materials for next to nothing or, in some cases, for free. Look for buildings that are being torn down, plots of land that are being cleared and the like to find wood, bricks or metal to create a fence. You'll still have installation costs associated with these types of fences, so they aren't completely free, even if the materials are.
While the initial expense of vinyl fencing is much higher than chain link or found materials, the advantage is that vinyl fence is maintenance free, as it does not have to be refinished or repaired due to rot. Vinyl fences typically cost twice the price of a wood fence, but over time, you'll save money on paint, stain, and other materials associated with maintenance, so you'll recoup that initial cost.