The key to cooking fluffy mashed potatoes is minimizing the amount of water they absorb. 

First, if boiling, start the potatoes in cold water so they cook evenly, and the outside isn't immediately exposed to hot water. 

Second, you always want to simmer the potatoes, not boil them.  

Third, always drain the potatoes well.

Try boiling whole potatoes or boil them in large chunks. This reduces the amount of surface area that comes into contact with the water and thus reduces the amount of water the potatoes absorb. 

Milk and butter lend mashed potatoes their richness and creamy flavor, and it's hard to add too much of either. To ensure the potatoes stay hot, warm the milk and butter in a small saucepan before folding it into the mash, otherwise the cold dairy cools down the hot potatoes. Make sure to stir the dairy in just until combined, as every time you stir, you lose a little fluff and gain gumminess. For super creamy potatoes, sub some (or all) of the milk with heavy cream and/or add more butter.