ive posted a reply to this q before, so ill justcopy and paste.
June 1st is fairly early, which is good, especially if you're advisor is a *****. Start asking now for letters of recommendation from old professors. Each school is different about collecting these. At my school, there is a pre-health advising committee that all the letters are sent to. After they received my letters, I arranged an interview with them and they wrote a committee letter. They mailed the committee letter and letters of rec. DIRECTLY to the schools (which REALLY helps not going through AADSAS). Most schools say they prefer getting them through AADSAS, but none complained about getting mine separately and they seemed to get them A LOT faster. Having them sent directly to the schools also helped me to avoid the problem of AADSAS losing the LOR's. If you do a quick search on here, you'll see that AADSAS loses some of the LOR's and that can really put a hold on your application.
Ok, on to step 2. If you haven't already, take the DAT by mid-may. You can take this any day of the year pretty much. It's offered on a computer at various testing centers. The AADSAS website offers information on where to register and such for that.
Step 3. Mid-May-Start filling out the AADSAS application. It's online so they don't send it to you. If you want to have your app. submitted on June 1st, this leaves you 2 weeks to fill out the app. Have ALL college transcripts sent to AADSAS in mid-may. This helps cut down on waiting time as well. You can start working on your personal statement now so that you have it ready when you fill out the app.
Step 4. June 1st. Submit application. Have your advisor send in LOR's. Make sure DAT scores are being sent to all schools you are applying at. Wait forever ("4-8 weeks" but mine took 9 weeks and others took even longer) for AADSAS to process your app. If you get it in the beginning of June, it will probably take less time because most applicants wait til late-July through Sept. to submit apps.
You'll probably start getting secondary applications (some schools have another small app. to fill out) and fees in the mail. Send these back ASAP. A couple weeks later, you will probably hear about interviews. This timeline varies though. I submitted my app. in late July, had it sent to schools late Sept., heard from schools the first week of Oct. about fees, and then about 2 weeks later I got interviews. All 4 of my interviews were scheduled for November (I then rescheduled one of my last choices). On December 1st, dental schools start letting people know if they were accepted! The first batch of acceptees has about 45 days to accept the offer, then the schools lets others know if they were accepted. This cycle repeats until the class is full.
For now, you have time to strengthen your app. Get shadowing hours in, work on your personal statement, study for the DAT (buy a Kaplan book), and research schools. Researching schools and figuring out which are the best fit for you before applying can save you a lot of money in the long run. There's more info here
https://aadsas.adea.org/aadsas2006/logon.html. Good luck!