Best way to gain muscle?

To build muscle, you need two things:

1. Calories to provide the energy and building blocks of the new muscle cells, especially from protein
2. A reason for the body to use these calories to create muscle and not fat, in the form of a resistance exercise program

For some people who are very overweight, the calories to create muscle cells can come from the body's existing fat cells, but most people need to simply increase calories consumed to provide what's needed. Unfortunately, there's a limit to how fast a body can add muscle, so eating more to try to speed up the process doesn't work beyond a certain point. Try eating 250-500 calories per day above whatever is needed to maintain your weight, and make sure you get sufficient protein, at least .7g/lb of bodyweight.

For the exercise component, weightlifting is an obvious choice, but swimming, hiking, gymnastics or calisthenics, each of these involve trying to overcome gravity and thus qualify. It really does not matter if you do short bursts at max intensity (lifting super-heavy for sets of 1-3 for example) or longer periods at a more moderate intensity (lifting medium-heavy for sets of 10-12), both will make you stronger, make you gain muscle. What matters is setting up a program which allows you to improve over time by making the body work just a little bit harder than before as you gain fitness.

This thread contains a variety of ways to increase protein intake.

This thread contains a variety of exercise programs you can select from, based upon fitness level, available equipment, and interests.

This thread contains a variety of ways to increase the intensity of a workout beyond simply "lift heavier or for more reps". It's designed with lifting in mind, but some of the principles apply to other types of activities as well.

Just remember that gaining muscle is not an overnight thing. It will take time, it will take effort, it will take consistency. But trust me, the gains will come to those willing to do the work, and they are worth it!