The following is in no particular order.
Start out at the bottom, with the easy hikes, and work your way up to the hard hikes. All too often, amateur hikers are eager to "climb the tallest peak" or "hike the longest hike" without any idea of what they are getting themselves in to. It's much better to start out with simple hikes, and slowly build experience and confidence, then it is to completely surpass your experience level on your very first hike and put yourself in a potentially dangerous situation.
Always turn your car around and park facing out at the trailhead
before you being your hike. If you get stuck in mud or snow while turning around, you want it to happen in the morning before you start hiking, not in the afternoon/evening after a long hike.
Keep a spare key duct-taped somewhere to the exterior of your car. If you carry your car keys with you in the woods, it's only a matter of time before you'll lose them.
You don't always need the fanciest, most expensive gear. In fact, quite often, the fanciest, most expensive gear isn't the best gear. And don't worry, if you stick with the sport of hiking, eventually the day will come when you can finally walk into a gear store and walk out without buying anything... because you've already got it all.
Explore. Get off the beaten path. Select hikes not because they guidebook recommends them, but because they look interesting on the map. Realize that there is a lot more opportunities out there than just the "tallest peaks" or those peaks above 4,000 feet.
Take the time to educate yourself in leave-no-trace, minimum impact hiking and camping techniques, wilderness ethics, and recreation aesthetics. Understand that hikers, through over-use and loving the woods to death, are the greatest threat to the resources we cherish in the backcountry. Work towards building the education, experience, and skills necessary to minimize your impact and respect the resources. Understand that you'll still enjoy your trip even if you aren't camped out right on the shore of the lake. When hiking, do the rock hop. If no rocks are available, walk straight through the mud, not around it.
Keep your feet dry. Wear waterproof boots or hiking sneakers. Try on lots of shoes before you select a pair to ensure a good, comfortable fit. Wear wicking socks. Wear gaters to keep mud and water out of your boots. Bring dry, clean socks to wear at night while sleeping, and keep your feet bare in camp for at least 15 minutes each night to let them dry out. Your feet will thank you. Lieutenant Dan wasn't kidding when he said "There is one item of G.I. gear that can be the difference between a live grunt and a dead grunt. Socks." Dry feet are happy feet.
Realize that you will get wet when it rains. If it's warm out, enjoy it. If it's cold out, be conscientious of the dangers of hypothermia. Pack covers are worthless, if you really want to keep your gear dry, use a waterproof pack liner or waterproof stuff sacks.
Drink lots of water. 4 liters a day minimum. It's better to take water breaks often, drinking a small amount each time, then it is to take few water breaks and gulp lots of water down during each break. Camelbacks can help you to drink more water more often, but they can also leak (I find that platypus is the best brand to go with).
Keep snacks handy to munch on all day. Hiking consumes a lot of calories, and your hikes will be much more enjoyable if you don't allow yourself to slip into a calorie deficit during the day. Combat the "post lunch fatigue" (the period of time after lunch where your body is expending more calories to digest your food than it is getting back from that food) by having a sizeable snack break half an hour before lunch.
Take the time off from work to do a midweek hike. You'll have the woods all to yourself and will love it.
Once you have the skills and are comfortable with the idea, take the time to do a serious overnight (3+ nights) by yourself in a remote area where the odds of running into other hikers is slim. It can do amazing things for your mental well being. You'll find an inner calm and peace that you didn't know your mind was capable of achieving. Even if you normally hike with a significant other, forbade them from coming. Even if you can't stand the alone time during the first night, don't let yourself leave the woods. If this makes you feel extremely vulnerable, exposed, and uncomfortable at first, realize that these are good feelings to have. You can only reach that inner peace if you confront these feelings head on by sticking it out, rather than avoid them by leaving the woods.
Join hiking clubs. Find other hikers with more experience than you who are willing to share that experience.
Understand that most backcountry campsites and shelters are first come first serve, and that it is never a guarantee that they will be free. Always have a backup plan in case the campsite or lean-to you planned on camping at is taken. Plan to arrive at camp early enough in the afternoon that you can put your backup plan into motion with plenty of daylight left if need be. Understand that camping primitively takes a lot more time and effort to do correctly than camping in an established campsite, and that sooner or later, you will be forced to do it. Remember that arriving at the campsite or shelter you wanted to stay out only to find it occupied is
never an excuse to camp illegally or in a manner that generates an unacceptable amount of impact.
Don't expect to be able to carry a full pack over a big mountain on one of your first hikes.
Trekking poles might not seem like they do much for you if you only use them for five minutes, but after the end of a long day with them in hand, the difference will be noticeable (and amazing!).
Commercially-produced backpacking meals are sometimes over-priced, and often over-salty. You can do much better for yourself by shopping at your local grocery store. Fresh fruit in the woods is worth the extra weight. Bananas will last a day or two, apples will last up to a week. Cheese will last up to a week if you don't touch it with your skin. Don't forget veggies to mix in with dinner!
Even if you use a GPS, take the time to learn backcountry navigation with a map and compass. It could save your life. Also don't expect your GPS to help you get un-lost if you haven't taken the time to learn the ins and outs of how it works before bringing it on a hike.
Take the time to read about the history of areas before you visit them. Often times, in the northeast there are lots of relics and historical artifacts of a time long gone hidden in the woods that most hikers march right on by without ever realizing they were there. Take the time to poke around in old lumber camps, at former backcountry ranger stations, etc., and be respectful of what you find.
Realize that you may need different gear for different seasons. A summer sleeping bag won't keep you warm in winter (or spring or fall for that matter!).
Don't hurry yourself into winter mountaineering too quickly. Know how to properly use an ice axe and crampons before you carry them with you on a winter hike and attempt to use them. People have been hurt badly (and even killed) because they were using technical ice gear without the proper knowledge and experience to use them safely, in situations that they were completely untrained for.
Bring a camera. You'll be glad years later that you took to the time to take photos of your trips- even the short ones that were just short walks in the woods for an hour or two.