Well, this is an easy one, or at least it is if by when you say "building muscle" you mean on a significant scale and more than just toning up or rehabilitation work. The answer being weights, weights and more weights! How you use them though is much more of an exact science.. Lifting any kind of weights in any configuration will on some level "build muscle" but as a general rule of thumb:
Lifting heavy weights for fewer repetitions will encourage greater muscle strength with some size increase.
Lifting medium weights for greater repetitions will encourage greater muscle size with some strength gains.
Lifting light weights for many repetitions will encourage muscular endurance with minimal size and strength gains (compared to the above).
For a more in depth view on this, please see our related blog (here).
To aid with any of the above you can go down one of two routes, the home multi gym or a weight bench with weight set (also known as free-weights). Some say it is better to start off on a multi gym and then progress to "free-weights" and this is usually due to the nature of a multi gym and how it guides the user's movement, so it is difficult to get the exercise badly wrong. The easy to select weight plate system (the stack) only adds to this and of course from a safety point of view, the cable and pulley set-up keeps the weight stack away from your body. With a free-weight system however, you are in full control of the weights at all times, often with the weight directly above your body or head so the responsibility is entirely your own and this includes the lifting movement itself, control of the weights, security of the discs on the bars and selecting the right amount of weight for the lift you are performing. On the plus side though, because of all this, a greater effort is needed to stabilise the weight thus recruiting more muscle and indeed other muscle groups as well, so the carry over here is a bonus. You may well find that if you can (for example) bench press a particular amount of weight on a multi gym, you are unable to do the same on a bench using free-weights.
There is a third, lesser known way of building muscle which can also be very effective for the right person and that is by using only your own bodyweight (press ups, pull ups etc to name but a few very basic moves) and it is an excellent path for some, but for others it could be difficult to get into (especially if you are overweight) and can also be limiting in how far you can progress (if you are slight of build) without eventually adding free-weights into your routine.