Step 1: Open up the in-game Options menu (default: Esc) and select the Gameplay tab.
Step 2: Check the box next to "Monster Power" to enable it.
Step 3: Open up the Quest Selection window.
Step 4: Select your designed Monster Power level from the drop-down box near the bottom of the window, under "Difficulty Setting."
Step 5: Once you've set your Monster Power level, quest, and difficulty, click "Select Quest" to confirm.
Step 6: Enter game and profit!
"No Monster Power" is the default setting. Each Monster Power level will increase the health and damage of monsters, and in return players will receive scaling bonuses to experience (for heroes levels 1-60) as well as boosts to Magic Find and Gold Find (for heroes in Inferno) which will stack above the 300% cap. The option to increase Monster Power will be available to all players starting at level 1 and can be adjusted separately for Normal, Nightmare, Hell, and Inferno difficulty.
(Note: If you join a multiplayer game, you will adopt the Monster Level of the party leader. When you leave the party, your Monster Power level will automatically revert back to your previous setting.)