There are 2 parts to a good exercise program: cardio, and weights.
You can do cardio, if you have space in your house, with some good aerobic style DVDs free from the library. The added benefit is that you can borrow a bunch until you see what you like, or rotate them so you don't get sick of the routines. The other option, as others have said, is walking. Lots of malls open early for people who want to do what you do - just walk constantly - which is great in bad weather. Don't stop & shop of course, and carry your wallet & keys in a light backpack so your hands are free (don't leave them in the car - thieves target malls and gym parking lots). Wear layers so you can tie a light jacket around your waist as you warm up. Set a time goal or a distance goal. You can get a $10 pedometer at most discount and sporting goods stores. Your ultimate goal is 10,000 steps per day but start with a smaller goal like 2500. Take the stairs when you can, part much father away from the store than everyone else, walk the dog (or a neighbor's dog or volunteer with some shelter dogs) and do anything else to increase the number of steps you take in your daily life. Do not get discouraged! Just try to make each day a little more energetic than the day before.
For weights - you can buy a light set that can add different weights. Get a DVD that teaches you proper form and ways to protect your back. This is extremely important. You don't want to get injured. Weight training builds muscle, and muscle burns more fat. It also can add some pounds so, no matter what, resist the urge to get on the scale all the time!! Let the mirror be your friend, and let the scale be your enemy. Weight training is important in the prevention of osteoporosis too.
For a few laughs and inspiration, watch the old Bette Midler movie, "Ruthless People" - she is held hostage in a basement while her inept kidnappers await ransom money from her husband, who doesn't want her back. So out of sheer boredom, she comes up with some creative uses for household items in a workout plan. You might get some ideas there! Just be safe if you do this so you don't get injured.
Look again at gym memberships - they're going on sale now because everyone freaks out in December and gets into a fitness mindset in January. I pay $19.99 a month for basic facilities - no pool. I have access to the machines for both cardio and weight training, and usually one or two personal training sessions are included for new members. There's always free orientation or reminders on the machines - just ask the person at the desk if you don't know how to set something. I also can take free classes for most things, and there's a group of almost all women that meets 3 times a week, so it's pretty entertaining and supportive. Sure, the gym wants to sign you up for personal training which is where they make their money, but I just say no and they leave me alone.
Sometimes a YMCA or JCC can offer cheaper memberships if you don't want all the features of the center. If you don't want the pool and racquetball, sometimes basic access to just the treadmill-type machines is fairly inexpensive. These places also often waive an initiation fee too. Look for coupons and ask questions.
Also make sure you are eating - too often, when we want to lose weight, we cut back our calories so much that our bodies go into "starvation mode" (part of the evolutionary response to famine) and the metabolism slows down, increasing fat retention. So be sure you are eating a good mix of protein and healthy fats (olive oil, nuts, avocado, fish, etc.). And you probably need to eat 5 times a day, just smaller portions.
Stay hydrated too - use water, not diet sodas or caffeinated drinks. Avoid most "energy" or sports drinks - they are heavy in caffeine, sugar, and sodium, as well as dyes. There is no scientific basis to most vitamin drinks either. There are a few available direct from the manufacturer that have really good hydration properties, even better than water due to cellular absorption and support, but you won't find them in stores. Cutting out a lot of unnecessary purchases can give you money towards a low cost gym too.
Most weight loss supplements are not tested, or they "work" with way too much stimulation of the central nervous system. The only ones that work are truly a nutritional approach to nourishing the cells and fueling them, not just metabolism boosters. Again, there are a few available from the food science companies that are balanced and safe, but you don't want to put your money toward supermarket or health food store formulas that aren't proven clinically.
Don't get discouraged - that's the main thing! Set reasonable and small goals, and if you exceed them, great. Then set a new one.