I had everything ready for the day the PTCAS application opened, and it took me about a week or a little less to get through it. Just make sure you've looked over the application to be able to make sure you have an idea of what you need to submit. Get your transcripts sent ASAP, and it shouldn't take too long to process them (once they arrive). I think it took somewhere between 3-5 weeks to process mine if I remember correctly. Also, take the GRE before PTCAS opens, so you don't have to wait to send your scores out. You can submit your application without having your rec. letters submitted, but you will want to make sure that the people writing them for you know that they need to be submitted somewhat quickly so schools can look at your application. Give the writers plenty of time to write before PTCAS opens and then they can just fill out the evaluation form PTCAS gives and upload the letter into the comments section.
All in all, as long as you get things rolling, you can fill out what you need to fill out pretty fast. I would say the rest of it takes about a month after you're done. Just remember, the faster you can complete all parts of your application, the faster schools will review your application, and the faster you will get interviews, especially for those schools that have rolling admissions. Good luck!