It really shouldnt take all that long, there are many fundamentals in tennis that you should learn. Tennis lessons are pretty expensive, but if you want some good, free tips, I will suggest my site, 

http://topspinsports.com. It offers Free Online Tennis Lessons all from qualified pros. Good news is that I personally screen the content so that it is top notch information. 

Really I would look at the pro "Basic Skills" or the url http://topspinsports.com/authors/16/Basi… This is all the fundamental stuff you may want to learn before your tryouts. 

I would expect it takes you 3 months of solid practicing and hitting under the right fundamentals. 

Good Luck and hopefully you enjoy the site

Thanks,
Steve Viglione
USPTA Pro