First you'll need to build a baseline amount of muscle from which to build strength. Make sure you eat enough protein (at minimum, 1g/kg bodyweight, or about 1g / 2lbs. bodyweight), and start slowly. As mentioned above, wearable weights can offer some kind of consistent stimulus for your body to adapt itself to, i.e., build muscle and reinforce bones and joints.
As you get stronger, you'll want to add in weight training. In terms of building pure strength versus "bulking up," (which won't happen anyways - women tend to build denser
muscle instead of sandbags) higher weights, lower reps training dominates. It may sound a bit intimidating but it's really not. Just find a weight at which you can do only one rep with good form. Then use this calculator and chart
to find out how much weight to use to do five reps. Then do 3-5 sets of no more than 5 reps. When you get to the full number of reps (25), it's time to move up the weight by a little bit. That's the basic structure. I can outline a couple exercises if you want as well, but I don't want this post to get too long.
The higher-rep training (10-15 reps) that's written in most magazines builds a lot of muscular endurance - being able to repeat the same action over and over again - rather than real strength. It increases your resistance to fatigue, but unfortunately it won't help you move a heavy bag of groceries from the car to the house.