Place your hands in the proper position. Your left index finger rests on the "F" key. The left middle, ring and pinky fingers rest on the "D," "S" and "A" keys, respectively. Your right index finger rests on the "J" key. The left middle, ring and pinky fingers rest on the "K," "L" and ";" keys. This position is known as the "Home" position.
Type a combination of letters using only the letters from the left side of the home position (F, S, D, A). Looking at the keys as you type is expected at this point. Once you have a row of letters, move the cursor below. Attempt to replicate the line above, this time without looking and only using the proper fingers (i.e., index finger for "F"). Practice until you are able to perfectly replicate the top line without looking.
Repeat Step Two using the letters on the right side of the home position (J, K, L, ;).
Repeat Step Two again, this time using a combination of the letters on both the left and right hand home position.
Repeat Step Two again. This time, add spaces in your initial row. Practice typing the letters and inserting spaces by using your thumbs to operate the space bar.
Repeat Step Two again. This time, use the keys above the home position. For example, the "Q," "W," "E" and "R" keys are operated by the left pinky, ring, middle and index fingers respectively. Repeat the process on the right side with the "J," "K," "L" and ";" keys operated by the index, middle, ring and pinky fingers of your right hand, respectively.
Continue to repeat Step Two, each time adding new keys. The idea is to use the finger that can reach the individual keys the quickest. For example, the index finger on your left hand is used for the "F," "R," "V," "T," "G" and "B" keys. The index finger on your right hand is used for the "J," "I," "M," "Y," "U," "H" and "N" keys. Keep practicing different combos until you know where each key is without looking.
Repeat Step Two, this time adding numbers. Use the left pinky for "1," the left index for "2," the left middle for "3," the left index for "4," "5" and "6," etc.
Repeat Step Two, this time using capital letters. You will accomplish this by holding down "Shift" with your pinky finger on either side of the keyboard and using the appropriate finger to press the right key. The difference here is, since your pinky is occupied, you will use your ring finger to strike its dedicated keys.
Practice whenever you can. The key to learning to type quickly and without looking at the keyboard is repetition. With enough practice, most will be able pick up the technique.