I used Acclaim for the Inaugural Star Wars Rebel Challenge at
Disneyland back in January 2015 and I registered in 2014 since I was between annual passes at the time and did not want to risk the race selling out the day it opened to the general public. I know that the process has changed since I last did it. The other key to remember is that there is some sort of requirement such as minimum night stay on Disney property and/or theme park tickets. Sometimes they can waive the theme park ticket requirement with proof of an annual pass. When I did it, I was required to buy a one day ticket to Disneyland at face value that could be upgraded.
If memory serves, the new procedure is that you call them, they take your payment information and advise you of any requirements such as hotel stay and/or park ticket(s) and so forth. After they have taken the payment which will include race registration and at least a down payment on the required hotel stay, you should receive a link from runDisney to register for the race in question. It acts the same way as the usual runDisney registration process only it shows you that you have already paid for the race. This is where you enter proof of time, shirt size, demographics, et all. You can also prepurchase any available race merchandise if you want to.
While it has been a few years since I used Acclaim Travel, I had a great experience with them. I used them near the peak of the runDisney registration insanity and watched the next morning as the races I had registered for just one day earlier sold out within 2 hours of the link going live. I have always been able to use the AP registration since that time, but would not hesitate to use Acclaim again if necessary.