Let's go camping!
Few statements in life are more capable than invoking the "flee or fight" response in people that those three words, "Let's go camping."
Some people love it, and some hate it. I've been a dedicated camper for most of my life. I was lucky; I grew up with a father who knew how to camp. I'll take a week of camping over any other style of vacation. I can camp anywhere at anytime. I've camped in the mountains, on the prairies, the desert, and in the arctic. Summer, spring, winter, and fall, I've camped in all four seasons.
Not all forms of camping are for everyone. An inexperienced novice probably won't enjoy a week in the bush, living off the land with nothing but a map, a compass, and a trusty knife.
For the first time camper, I'd recommend an overnight stay, or a weekend at a State, or National Park. With the convenience of the internet, it's easy to check out campgrounds in your area, and see what amenities the campgrounds are equipped with.
Once you've decided where you are going, the next decision is how you are going to camp. There are two choices, tenting, or RV. I don't recommend using your vehicle as your shelter.
Tents
Go to the sporting goods stores, and look at the tents. Some of them even have some of their tents already set up and on display. How many people are going? You don't want to try to cram three people into a two-man tent. My rule of thumb for tent size is to add one to the number of people in your group, and look for tent of that size. So, if three are going, I'd look for a four man tent. For larger groups, two medium size tents is easier to deal with than one huge tent.
Don't be guided strictly on price. This rule is pretty much true for all camping equipment. Quality gear will cost a bit more, but generally it's worth the cost.
Once you've purchased your tent, take it home and set it up in the back yard. Take it down and set it up again. Know your equipment. The last thing you want to do is get to the campground when it's dark and try to set the tent up for the first time, reading the instructions by flashlight.
I'd highly recommend buying tent stakes separately. Generally the ones that come with the tent are flimsy at best. Wal-Mart, and other sporting goods stores sell stakes that look like big spikes, and are fairly reasonable. Don't forget to pack a hammer, or a hatchet to pound the stakes into the ground.
Sleeping Gear
Other than the tent, the sleeping bag is most important piece of gear. If you're not warm at night, you're not going to be comfortable. Most sleeping bags are rated to different temperatures. Know the type of weather you are going to be in, and buy your sleeping bag with that in mind. Don't buy a bag rated for 40F when the lows are going to be in 20F range, and don't buy an Arctic mummy bag rated for -50F when the lows are going to be in the 40's. Again, don't let the cost be your only guide. A good sleeping bag will cost a little more, but will give you years of service.