Registering takes two steps, but even if you don't know the exact date you want, you should do the first step sooner rather than later. The first step is registering and paying through the ADA website. They process a week's worth of requests on Tuesdays, and will send you a confirmation on the Tuesday after you register. The second step is going to the Prometric website and selecting a date.
You still have time - I signed up through ADA on Monday and today I selected July 7 for my test date. Availability is different depending on where you live - in the Boston area, there wasn't much availability in June, but there was a lot in July and August.
Also, keep in mind that you can reschedule your test date until 2 days before the test - the fee to reschedule is $25. So right now you could select Aug 10 to reserve a spot, and if you feel you're not ready as the test is approaching, it's no problem to push it back.