Hi Veggie Girl,
A squat machine is specially designed piece of gym equipment just for squats. I absolutely LOVE it! It's my all-time favorite machine next to the bench press. It's hard to describe, but I'll try. You stand on a gritty-textured platform and get under the "handlebars". They're like handlebars on a bike with a brake on one side. There are pads that fit over your shoulders and a padded back. There's a stack of weights in front of you. You select the weight you want, hold onto the handlebars, squat down and you'll hear a clicking sound. When you get to 90 degrees with your legs, lift and begin. When you are done and in the down position, squeeze the brake and it will release the weight so you can stand with no weight.
I like it because I don't have to worry about form and hurting myself. I can also lift really heavy weight (heavy for me!), which is what I like to do. There's no way you can duplicate the machine at home that I can think of.
If you're working out at home, lunges with dumbells would probably be really good. I was doing sumo squats at the gym but the weights I needed were too dang heavy to hold so I had to switch to the Smith machine. Sumo squats can be done at home with a dumbell. It's a variation of a squat where you hold one dumbell with the end down between your legs. Feet are pointed somewhat outward, making it target more of the inner thigh (which is what I wanted). I just had a heckuva time holding a 55lb dumbell. I'd be over in the "guy's section" of the gym and they'd look at me like, what is she doing???? Sumo squats are also called plie squats. I think that's how you spell it. Dumbells are very cheap, if you get the iron ones. The next time you are at a sporting goods store like Academy, try a Sumo squat and see what weight you would need. Or if you even like doing them. I liked doing them because they just felt good, but I could never get enough weight.
Just a suggestion....