Choose the two songs you want to beat mix. When learning the technique, it's easiest to select tracks with similar tempos.
Play the first record. Start the second track on the other player.
Listen to each song. The first one over the speakers and the second through your headphones. You must be able to count beats and recognize the first one of each measure.
Count along with the beats until you have the exact timing of each second song. Focus on the beat of the snare drum. This is the easiest one to match.
Figure out which beat the snare drum is on. Get the count down and when it'll match up, start playing the second song.
Find the first main beat of the second record. Some DJs will physically mark it on the record with a sticker. Hold the record still at the first beat and pause the sound. Let it go at the desired beat of the first song.
Play with pitch control while both tracks play. Listen carefully to see which beats are off. Adjust pitch control to alter the tempo until the beats match.