Buy a set of direct-drive turntables, as opposed to belt-drive turntables. Although it is technically possible to mix on belt-drive turntables, it is far harder. The belt acts like a taut elastic band when you try to spin and scratch records, meaning you do not get the same control as with direct-drive turntables.
Connect a mixer to your turntables and amp. The key component of the mixer is the crossfader. This is a sliding switch in the middle of the mixer that allows you to choose which channel is audible. The crossfader is locked (only one turntable audible) or open (both turntables audible).
Place a slipmat on each turntable. The slipmat goes underneath the vinyl.
Choose two records that play at the same RPM and have the same beat structure. The most common beat structure is 4/4 (four beats per bar). Place a record on each turntable and set the left one spinning. Keep the crossfader locked so that only the left turntable is audible.
Plug in your headphones and put them on. Start the right turntable spinning. You will now be able to hear the right turntable through the headphones and the left turntable through the main speakers. It is best to only cover one ear with the headphones so that you can easily hear the left turntable.
Use your hand to control the speed of the right turntable. Try to make the beats match those coming from the left turntable by slowing down or speeding up the vinyl on the right turntable with your hand. Once you have matched the beats, use the crossfader to open up the right channel. Both turntables will be audible through the speakers.
Set the crossfader back into the locked position. Both records will be playing in time but only the left turntable will be audible through the speakers. Put your fingertips on the right-hand record and bring the turntable to a stop. (The power is still on, so you are physically stopping the vinyl from playing.)
Use your fingertips to push the right-hand record back and forth in time to the beat of the record on the left turntable. Move the crossfader back into the open position. Both the left-hand record and your scratching will be audible through the speakers. This is the most basic type of scratching and is known as the baby scratch.
Practice other types of scratching. Stab is where you move the crossfader back and forth, from open to locked, quickly, so that only the forward motion of your scratching is audible. This requires some dexterity and creates a high-pitched scratch underneath the record playing. Chop is similar to stab, only you do not push the right-hand vinyl forward, you simply release it. This way snippets of the right-hand record are scratched into the record playing on the left turntable.