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Before you set out for a multi-day trip, try a couple of day hikes through various kinds of terrain and weather to find out how it suits you. It's good idea to make sure you enjoy hoofing around out in the woods before you find yourself out in the middle of a 14 mile loop in the wilderness.  Try a few hikes without any gear, but plenty of water, light snacks, a map of the area, and the right boots. Go out for a mile or two with some friends and have fun. If you like that, try going on a longer hike, for several miles of somewhat rougher terrain. If you like that, take your bag with you and see how you enjoy it. Gradually build up to a series trip. Are you interested in the mountains? The grasslands? The great lakes? Depending on where you live, the backcountry may be close by, or you may want to venture out farther for a serious hiking experience. In most areas, you shouldn't need to travel more than a half a day by car to find a good National or State Park in which you can hike and camp.  Pick an appropriate time of year for that destination, as well. Some destinations are very crowded at certain times of year, or around holidays, while others are inappropriate for backpacking at certain times of the year. It'd be bad to head out to the desert in the middle of the summer if you're a first-timer.  It's also usually good to avoid areas with bears during bear-heavy seasons, which will vary from region to region. Want to hike the Cumberland Gap? Explore Yosemite? Pitch a tent in the Grand Tetons? Once you've settled on a particular region of the country you'd like to explore, pick an area that's appropriate for backcountry camping. Within the US, here are some of the best destinations for serious camping:  Yosemite National Park, CA Joshua Tree, CA Denali National Park, AK White Mountain National Forest, NH Olympic National Park, WA Zion National Park, UT Glacier National Park, MT Big Bend National Park, TX Different wilderness areas and parks will have a variety of options available to backcountry hikers, so consult park maps of the area to find the specific trails, or find some online by checking out the National Parks website. Typically, long hikes come in three styles, which you can pick based on the difficulty, the type of terrain, and the sights that you may want to see at your destination. The three basic types of backcountry hikes include:  Loop hikes, which follow a long circle that will allow you to end up back where you started. Out and back hikes, during which you'll hike to a specific destination and then retrace your steps backward. End to end hikes usually require leaving a car at both ends, or arranging pick-up at your eventual destination. This is only typically done for very long hikes that go through multiple areas. While you might want to jump right in and do something difficult, you'll need to consider the terrain, weather, and the experience and conditioning of your group when planning how many miles you will travel each day. Most trails are rated for difficulty, so you'll usually want to stick with anything at a level 1 or 2 for your first several hikes. They'll be challenging enough.  Novices and weekend warriors should plan on hiking no more than 6–12 miles (9.7–19.3 km) per day of a given hike. In relatively tough terrain, that'll be more than enough. Experienced hikers in good shape can sometimes do 10–25 miles (16–40 km) per day, depending on terrain, but it's usually best to not push it. If you're camping on public land, there will typically be a small fee associated with coming into the park itself, and another fee associated with camping. They're usually pretty small, and you can get away with no more than $15 dollars or so a night, depending on the season.  At most parks, you'll have to display a permit on your car while you hike, and something on your tent, or bag, as well. The local regulations will be explained to you when you check in to the ranger's office upon your arrival. Most National Parks and other public lands will also have guidelines specific to their environments, at the time of year you're camping. For example, Yosemite National Park requires the use of bear-proof canisters for food. Campfires are great, so long as they're legal. Many areas prohibit fires during dry periods. At other times, they may only be allowed in specific locations, typically fire rings located at campsites. In some places a separate campfire permit is required to use a backcountry cooking stove. Never, ever, leave a fire unattended. Do not light a fire unless you have enough water available to extinguish it thoroughly.  As a precaution, clear a 15-foot (~5m) circular area around your fire, to prevent the wind from igniting any materials outside of your fire pit.

Summary:
Go on day hikes first, then overnight hikes. Pick a general destination for your backpacking trip. Pick a specific park or wilderness area. Plan your route through the area. Be fairly conservative with your routes and schedule on your first trips. Check to see if your destination requires permits or other advance preparation. Find out local fire regulations.