The long tail cast on is frequently called for in patterns and has many uses. It has a "right" side and a "wrong" side, and it requires that you estimate in advance the amount of yarn you will use to perform the cast on. This cast on can be done with either the right of left hand. (Left-handed demonstration begins at 02:54 in the video).
SET UP: Estimate how much yarn 10 stitches will take by wrapping the yarn around the needle 10 times. Take this estimate and use it to estimate how much yarn you will need to cast on the required number of stitches for your pattern. Add an inch of yarn for wiggle room and make a slip knot.
HOLDING THE YARN: Once your slip knot is on the needle and the needle is in your dominant hand, make sure your yarn is situated so that the short end is hanging to the front, towards you, and the long end (attached to the ball) is hanging to the back, away from you.
Make your other hand like a duck, and put it between the ends, so that the front/short end is over your thumb and the back/long end is over your fingers.
Separate your thumb and index finger, and grasp the tails of the yarn with your other fingers. Your thumb and index finger should make a wide V. Turn your palm upwards.
STEP 1: Insert your needle tip up underneath the strand running from your grip to your thumb, creating a loop.
STEP 2: Wrap the strand on the front side of your index finger around the needle tip counterclockwise, across the front of the needle.
STEP 3: Pass the loop on your thumb back over the needle tip.
STEP 4: Pull the loop snug (don't strangle it) with your thumb, and set up to begin again at step 1.
This cast on has a "front" side, the side facing you, and a "back" side that will show what look like purl bumps. Depending on your pattern, this purl/back side may or may not be the "wrong" side.
Cast on as many stitches as you need. If you have too much yarn left over, trim your tail to avoid knitting with it by accident! If you don't have enough yarn to make all your stitches, this is a bummer and I feel for you. An opportunity to practice some more?! Or, try the Endless Tail Cast On.