The art of 'mixing' is an acquired skill to the individual mixing!Marky is right - suggest you get two copies of the exact same track.
(If you want to have a 'go', although it really is best to get a little hand on advice...)
A very brief guide...
Lets imagine we have two tracks...Source A and Source B.
When you play source track A, the B track can be played exactly at the same time and thus, the 'beats should technically match'.
If you are playing an arrangement of 16/32 beats (say intros) before any change or instrument is added to the song, or vocals start to come in, etc, then the time to play Source B would be on beat 1 of the next 'measure' of 16/32 beats.
If we break down (simplify) the theory for a 16 beat 'beat match' 4/4 time:
Source A has a 4/4 bass drum beat:
1 2 3 4 [ 1 2 3 4 [ 1 2 3 4 [ 1 2 3 4
We count on the beat - not after the beat.
For the example, Source B is exactly the same as Source A, the 1st beat of the Source B track to 'come-in' after the 1st 16 beats would be thus:
Source A: 1 2 3 4 [ 1 2 3 4 [ 1 2 3 4 [ 1 2 3 4 [ 1 2 3 4 [ 1 2 3 4 [ 1 2 3 4 [ 1 2 3 4
Source B: * * * * [ * * * * [ * * * * [ * * * * [ 1 2 3 4 [ 1 2 3 4 [ 1 2 3 4 [ 1 2 3 4
----------------------------------------------------------^
So the first 16 beats of the Source A track has played and we have played Source B on the first beat of the next 16 beats.
(Example represented as 1....16 beats, counting 1,2,3,4.....14,15,16)
(This is only an example but for 'modern dance music', the song structure is usually 16 beats per 'measure')
Notes
A 'drop mix' is literally 'dropping' the next played track into the current played track - on the beat, where as the 'mixing element' combines fader and applied eq (bass, etc) for 'smooth' mixing.The theory changes when we want to add a track with a different tempo.
Players with 'pitch control' / 'tempo adjust' will allow you to mix 2 tracks of different tempo by simply '+' & '-' adjustment on an increment scale.
Master Tempo engaged on systems will allow you to adjust the tempo of a song without altering the vocal pitch.Whilst source A is playing, the DJ will listen to source B in the headphones to 'match and adjust the tempo' in order to beat-match the tracks.
Quick ways of finding the tempo to mix in with.
An element of maths can be applied to mixing (beat-matching) but I'm no Carol Vorderman!
Those with BPM counters will be able to glance at the Source A track and see that (for example) it has a BPM of 120.
If the Source B track has a BPM of 130, then the source B track can be reduced (-) on the pitch tempo scale approx 8%.
When two tracks appear to be matched but later go out of sync (running out) then this can be down to the fine tempo and arrangement of the tracks used, or, the beats were matched but not 100% perfect.
The 'human element' will adjust the tracks manually to accommodate difference - more later on about this.
Another way to 'mix quickly' is to use the drop mix (mentioned above) but it can sound quite abrupt if the tempo difference between the tracks is a mile!
Looking at the pitch slide (tempo adjust) scale, you may see notch's that have full and half increments. Some may be numbered.
The 2,4,6,8 quick 'slide and play' process is literally move the pitch to '+' or '-' 2, then 4 or 6 or 8 and playing the track in between (obviously!) to see if the track you are going to 'mix in' is close to the track playing. Finer pitch adjustment would then be required to 'smooth mix' the incoming track.
There are 'other ways', practice, practice, practice..... and then some, to adopt in mixing but some important points to note on such practices are:
Time delay
Phase
CueTime delay is the sound-lag from the speakers bouncing the sound back from the 'walls' of the venue before it hits your ears!
It will vary from venue to venue as every venue is different in layout, size etc.
A 'booth monitor' or 'fold back sound' system will help when mixing but not everyone can work with these. These are a great aid to reduce time delay as it represents the actual sound coming out from the speakers but is usually positioned towards the DJ.
(Like vocalists have sound monitors on a stage facing them to help them keep time with the music.)
Mixing in headphones - such as mixing both tracks in the ear piece before you open the source B channel fader is more common but then again, not everyone can do that either! It takes time and practice. Some will take to it like a duck in water.......etc.
The 'image' of the DJ with one ear covered with a headphone and the other ear 'open' to listen to the music playing is common too but that DJ has had to 'eq the headphones' to compensate and 'balance' both ears with the levels of music played.
Thus, if the music in the headphone was too loud or too low, it would be difficult to mix - not impossible, but difficult and of course, long term, damaging if the level is too loud!
Finding a happy medium is all important and individual.
Going back to the main point - if you have two tracks the same and start them both at the same time, and then start them a fraction of a second apart, a 'phase sound' will be/ can be heard.
To compensate this phase or to produce this effect, the tracks can be brought back into or out of 'phase' by adjusting manually either source. Some systems have jog dials/platters, pitch adjust buttons (bend) or + & - buttons.
Note the 'direction' of the jog dials for forwards (speed up) and backwards (slow down) - like a record, clockwise and anti-clockwise respectivly.
So if the source B track was the latter track to be played, we can either increase that track with the '+' adjustment to 'catch up with the other track, or in turn, reduce the source A track with a minus adjustment if required.
Overall, setting the right 'Cue' for the tracks played is really essential.
If the track played starts with a long drum roll or sound effect then a Bass drum beat, then the cue point can be set from the bass drum. The sound of setting the cue point (ready for play) can sound like a 'stutter' on the various systems used today, but it is the start of the 'stuttering' sound (the front of the bass drum wave form) we are looking for.
So, when the source B track is going to be brought in, you can press play (or the old quarter spin) the track to come in on that beat, matching the beat of Source A.
Although brief - hope this helps!