For what it is worth, Boy Scouts, who do LOTS of camping (pretty much the core of the Scouting experience) are taught to carry/use three different tools when camping:

1. Pocketknife - for food preparation, cutting small stuff. My son's troop recommends a locking blade. Younger Scouts tend to carry Swiss Army Knives; older Scouts tend to carry multitools (Leatherman & others). The screwdriver tools aren't much use, but the pliars get used a bunch. We tend to use real can openers rather than mess with those on knives.

2. Axe - mostly used to split wood and chop small 1-3 finger sized sticks. Any larger and it is much easier to use a saw to do the cutting. My son's troop tends to limit this to hatchets (battoning with logs to split larger wood) rather than axes, but my own bias is that hatchets are more dangerous than full length axes since hatchets have a slightly higher tendency to get close to fingers, legs, etc...

3. Bow saw - used to crosscut larger logs

If you want to learn how to camp, consider getting a Boy Scout Handbook, which is packed with simple but very usefull camping/hiking skills. If you don't know where to buy one the Chicago Area Council's web site is http://www.chicagobsa.org - call them and they'll tell you where to buy one.