All of this advice on listening for the end of bars or recognising the first beat of a measure etc. is correct but really the only solution is to do it by ear. Many of you are about to post a reply saying "..it's not the only way......" but sorry it is!, especially as when you are DJ'ing you need to be able to many things (EQ,beatmatch etc) instinctively in a split second(without having to count or calculate). These tips are good for trying to understand the theory when you're starting out but by the time you're good enough to play out these things need to be down and not pondered about. Some people do rely on these "tricks" but the DJ's who are the best, Feel the music, the speed of the tracks, the levels and don't have to conciously figure out what they are to do next. I developed some things that helped me when I started out:
1, Get two records that have large beat or percusson sections. Set the left deck (A) at pitch 0 then try to mix in the second record. Make a mental note of how much you had to slow or speed up it up. Then swap the records over and do same again.
Don't be afraid to touch the bender(cd)/record even if you don't know whether to speed up or down; when you get it right try to remember what you heard and this will eventually build an instinct of knowing when to speed up or down. Focus on what you did right.
2, You will find some pairs of records or even a record easier to beat match than others. This varies from person to person as our hearing and tastes are all different. (I found that simple beats where easier to match in the beginning) The only way to find out this is to go through your collection. This can also have the benefit of developing a sense of what will go with what and at some point you will realise that you don't have listen to the record to know whether it will go with another, you can do it in your head.
3, Time yourself at beat matching and try to get faster each time and before you know it you will get a better sense of which to speed up or slow down.
4, Try mixing other things like ambient parts of tunes over beats. you will be able to hear at the end of a bar or 32 beats a change (ie in the chords) and if the 32nd beat comes before that chord change then speed up the ambient track. if the 32nd beat comes after the chord change has allready appened then slow the ambient track down. This will develop your senses so you don't have to rely only on your ability to spot "out" or "clanging" beats.
5, Once you have mastered all these then you can do the real method of beat mixing: mix tracks WITHOUT TOUCHING THE PITCH BENDING DISC(CD) OR RECORD(VINY). This will take discapline. Only use the pitch slider to correct the speed. When you hear the record being brought in is going too fast, just push the slider back slightly further (try double?) back than you normally would and when the mix is back "in", bring it slighty forward so that this correct speed is maintained. It Works the same way (in reverse obviously) for tunes going too slow. This is the fastest and cleanest way to beat match and how all the pro's do it. I'm sorry about the phatness of this post but enjoy and good luck!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!