Weight work (in addition to aerobic activity) is definitely the answer. Since everyone describes it differently, I'll tell my favorites even if I'm repeating.
Take one weight in both of your hands, and lift it over your head. Keep your elbows as close to your ears as possible. Slowly lower the weight behind your head, then lift it back up. Repeat.
Put one foot ahead of you and lean over. If you have a weak back, support yourself by putting your palm on your forward knee. Have a weight in the other hand, and keep that elbow close to your body. Lift the weight behind you. There are many variations -- stiff arm, raising and lowering the weight behind you slowly. Or raise the weight as far behind you as you can, then pulse it a little, or just hold it there for awhile. Or combine the back movement with a forward one and turn it into a biceps curl as well.
You can start with as little as a couple of pounds and work up, but don't push it. And DO NOT go fast. With the exception of pulses (very small movements) you should always do weight work slowly. The downward movement should never be "dropping" the weight, but be equally as stressful as lifting the weight.
Oh, another good one, without weights, was a favorite when I was on the road. If you have a table (I used picnic tables when we were traveling) that is sturdy enough, back up to it, and lean your weight on your palms. Do backwards push-ups off of the table.
Sometimes it is worth it to put up with the sales pitch to take up your local gym on their free weeks. It is a p-in-the-a to listen to them, but quite often you'll get some good instruction. Just make sure you tell them you want to learn about "free weights" (which is what you probably have at home) and aren't interested in the machines, so you get what you need to work out at home!
I was the first woman I knew of to learn to use weights because using military gyms, the guys always thought I'd be good at it. I'm not in the best shape, but I don't have flabby underarms or inner thighs, in spite of being overweight.
Pilates is a great program for this as well.
Good luck. You'll never regret keeping your body in motion.