Well there was me thinking that I was going to get a quiet night in....then Paula comes calling

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Okay, first of all be thankful that you've found somebody who is willing to spend the time to train you

. D.J's like this, are very few and far between, although one thing to remember when you are learning the business is to maintain your individuality. Yes a good "mentor" will teach you the ropes and is certainly a must but make sure that you don't copy them and become a clone.
When dealing with other D.J's, remember that there is still a lot of ego and pride attached to the occupation, and those D.J's who will immediately view you with hate once you have announced that you are "in the job". Ignore these narrow minded individuals, but don't become one of these yourself when talking to them. Nobody likes to be made to feel inferior and if you come across as being too confident, big headed and appear to "know it all" then the other D.J is likely to be on the defensive.
With regard to training, my own trainees spend around 6 months on a part time basis purely helping out. During this time, they will either be purely observing how myself or Richard run the gig, or will be using the mixer, cuing up the next track etc - all under supervision. Then they will progress to the mic work. Usually in this period they will have seen what D.J'ing involves (the good & the bad!) and I will know that, by then, they have the dedication to carry it further.
On the whole my own trainees, will spend at least 12 months before they are allowed out to do a gig on their own. This doesn't mean that they won't be doing a good gig well before then, but I prefer to set a minimum period, since after all, they will be working under my name and reputation.
Depending on age and the individual, you could pick up D.J'ing in a few months, or it may take a few years. A year to pick up the basics is, in my own opinion, a little bit of an exaggeration, you could possibly be running your own successful roadshow by then. If by "D.J Teacher" you are refring to somebody who is being paid to teach you??, then I am a little sceptical about somebody who is being paid by you, telling you how long it is going to take, so soon into the course. I mean, he has a financial incentive to keep you on the course for as long as possible!.
My own training policy would roughly be along the lines of:-
Stage 1:- Purely observing, watching how the equipment and lighting goes together and how an experienced D.J runs an average gig.
Stage 2:- Using the mixer and cuing up the next track. How to set up and maintain adequate EQ settings for changing room acoustics (i.e people arriving and leaving). Finding the right point of a track (Removing quiet intro's), basic mixing and how to merge two tracks without mic intervention. (I'm not an expert in beat mixing although I can obviously bring in two similar tracks without crashing). I leave the beat mixing to another D.J -Chris (Prodical Son).
Stage 3:- Basic mic use, hold to talk into a mic, mic technique etc, this would probably just involve them making basic one line announcements such as "Buffet Ready", "Last Orders", "Taxi for Smith" etc. At this point I would also be asking them to suggest a next track to follow the current one. At first inexperience often shows, but when they start following a routine which works, then you know that they are starting to think AND read the dancefloor / Audience.
Stage 4:- More involved mic use, introducing tracks, announcements. Also basic technical routines such as changing fuses and lamps. common equipment faults and how to rectify or get around them.
Stage 5:- Running an actual gig by themselves, but with me still being present, at this stage the individual has usually being helping at least once a fortnight for the last 10 - 12 months. Sometimes it can take as long as 18 months before they are ready to go and do a show by themselves, other times it could be only 6 months for them to reach a semi - pro level. The 12 month philosophy is just my own training policy for peace of mind, but I have seen people who could easily do an average gig, long before then.
Remember that Mobile D.J'ing for an audience of all ages is more than just being able to beat mix. You may have a full dancefloor but the next track - although mixing perfectly into the last, could possibly have very adverse reaction and empty the dancefloor.
A good Club D.J will be able to beat mix popular tracks AND keep a full dancefloor. A bad club D.J will purely mix to satisfy his own ego and if as long as it mixes 100% and he can slap himself on the back, then to hell with the dancefloor.
For the average Mobile D.J at a Wedding Reception, then sometimes it is more important to mix the era's and play something for everybody!, rather than to actually Mix the TRACKS. Yes, it is possible to mix and do mobile work, but knowing when to change the music to a different era, and inform people of the fact by using a mic.
This is one of the main differences between Club D.J's working a Set at a popular nightclub, and the 5 - 80 year old mixed audiences at Ruth's 50th Birthday
Just my thoughts!