Gaining weight is simply a matter of a positive caloric balance. Basically, if you take in more calories than you burn, you will gain weight. As far as what kind of weight you will put on, this all depends on what you're eating. I'm currently in your same boat, trying to put on weight by the summer, so I'm eating huge meals, and downing weight gainer supplements post-workout and right before bed.
Muscle milk is a great protein supplement, but isn't the magic potion to help you gain weight. What would be best is to take the muscle milk along with a diet that is probably around 40% protein, 40% carb, and 20% fat. If you're not used to reading food labels, I would start. Make sure you're eating as much natural, "good for you" kind of stuff, like chicken breast as opposed to lunch meat, or whole wheat bread as opposed to white bread. Milk and eggs are the gold standard of protein, mainly because almost every gram is ingested into the body and used for protein synthesis. I drink milk like water, and have eggs every morning.
As far as exercising goes, what does your normal weight lifting routine look like? What kinds of sets/reps/exercises etc?