everytime after I've published a new article about squats I get lots of comments and mails from people who ask for advice, because they want to do squats for getting strong and toned legs, but are suffering from knee issues caused by injuries, overstress or misload in the past.
Actually I do have some recommendations for you, because I also had some issues with my knees when I was younger. Firstly try to start with "easy squats" like Jackknife Squats (a description is in my blog as well), but (different to the description) don't go all the way down. Stop the movement, when your thighs are parallel to the ground. Do them with a very slow movement speed (without momentum; pay special attention to the downwards part and don't dip down fast) and start with 10 to 15 reps (3 sets). This way the stress on your knees is not that high and your joints and tendons get time to get used to the squat movement (and get stronger meanwhile). Increase the rep number and the range of motion slowly every week until you can manage the target reps (as mentioned in the description). Then move on to Supported Squats and later to Full Bodyweight Squats without support.
Another important point is that you should pay attention to the position of your knees while executing the exercises. Don't let your knees travel inwards and don't let them travel beyond your toes at any time of the exercise.
An alternative exercise you can try is Split Squats (aka Lunges).
To get really stable knees it's also vitally important, that you take care of the back side of your thighs as well (they can cause knee troubles too). For strengthening this part, Kettlebell Swings are a great option as they train the whole rear kinetic chain. Make sure that you learn the correct technique first!
If you don't want to use kettlebells by now, the leg curl machine is a good thing for the beginning (I don't like machine training, but for getting started after having knee issues, this one is ok). Squats (and Sprints) train the back of the thighs as well, but for most people it is still a weak part (except you do squats and/or kettlebell stuff already) and should get individual training first/additionally.
I hope this could help you a bit! (Btw. Try the Trifecta as a stretching program...it improves the flexibility of the whole body, including legs, very fast).
One more thing: If you have serious trouble with your knees, don't hasitate to consult a physician before you start working out your legs!