First of all, I'm not saying that it is simple but if you had to put it in the most basic principles (without using the auto-sync), DJ'ing comes down to 2 basic things:
1. Making sure the speed of the songs matches each other (bpm)
2. Knowing when to start the next song (hitting play, cueing, etc)
The speed of a car is calculated in Km/H or Mph but the speed of a "typical" song is counted in BPM (beats per minute). The clock beats at 60 beats per minute (60 seconds in a minute). It also beats at 120 beats per minute (60 times 2 - where every 30 seconds is 60 beats).
A turntable, CDJ or a controller changes the speed in percentages so the easiest way to explain BPM would be if the song had a BPM of 100.
Let's say you are playing a song of 100 BPM at 0% (no change in speed) and you want to bring in another song of 102 BPM. Then you need to decrease the speed on your CDJ by approximately 2% so that both songs can match speed.
Luckily, you don't need to do that using math formulas or your ear alone. Nowadays, you have access to several softwares such as Serato, Virtual DJ, Traktor, Record Box, etc that show you the BPM of every song and the percentage that you are increasing or decreasing.
Once the speed matches, you now have to know when to play/release the song on top of the one playing. House music and extended versions of songs are the easiest options to explain this simply.
What makes music, music is the formation of loops or repetitiveness. That is why some artists (DJs, singers, producers, etc) are able to predict what is going to happen even if it is the first time they hear a song. I call it anticipation or even expectation. Sometimes it is anticipated or expected for the next note to be specific as it will complete the "feeling".
Hey, I'm doing the best I can here to explain something that we can only feel.
So 1 loop in every song is (1-2-3-4, 1-2-3-4, 1-2-3-4, 1-2-3-4) and then it loops again on and on.
Your goal is to match the (1-2-3-4) of the song playing to the song that you are going to introduce. House music and extended versions of songs usually all start with the "1" so it is easy to just match it to the song playing. However, not all songs start with "1-2-3-4". Some may start with "AND 1-2-3-4" but if you are able to locate the "1" in every song then add a cue in your Serato, Virtual DJ, Traktor, etc on the "1" of every song. This way you will always know when to start the song.
Of course, this is just a basic piece of information when it comes to becoming a DJ but I thought I took the time to explain it as simple as I could without going into music theory. Hopefully, you got some new information in this article and I'll see you in the next one.