Tons of exercises can be done at home!
For strength training:
You can start by doing body weight exercises to build basic strength. (Body weight exercises can be found so easily with a google search!)
And/or you can do Free Weight exercises if you have any dumbbells or a barbell, or are willing to buy some. (Those exercises can also be found on google)
For Cardio:
Walking, running, cardio machines (such as elliptical or treadmills), fitness DVDs, jumping rope, etc.
With that said they are both strength training are very important in losing weight and toning up so you should use them both in your program. Nutrition is also key in weight loss.