This is one of the simple ways to cut cards using only one hand. There are other more complex ways of cutting, but I only know of three ways of doing it and the other two ways that I know of, I kind of trailed off to other tricks before mastering them.
The only materials you need is a deck of cards and one of your hands (keep the other close by in case the cards start to fly).
Step 1: Position the Cards and Drop Half
Position the cards as shown in the photo. Use your pinky finger as a guide to prevent stray cards from dropping.
Now tilt your thumb forward until approx. half the deck falls into the cradle created by your hand.
Step 2: The Lift Process
Two of the photos below shows the underside of the cards.
The main photo shows how you start to push the cards that were resting in the cradle of your hand upwards. You start this process by using your index finger and push the cards up against the underside of the top half of the deck the you are holding. You continue to push until you've created a right angle (right against the thumb) as shown in the second photo.
You then lift the bottom half of the deck up and over the top half (remember to use your pinky to steady the cards) as shown in the third picture.
Step 3: The Reunion
Now that you have the bottom half in the control of your thumb, use your index finger to lower the top half down and use your thumb to gently push the bottom half over the top. The last two photos show how you use your index finger to lower the top.
That's all there is to it. If you get really good at it you can even reset the deck using only that one hand and keep cutting without ever using your other hand.