I have heard "I am guaranteed" to get in at my home resort. Does this mean I can call SS up to two months before a trip and know I will get my room?
No. In practice, something at some resort is generally available, but that is not guaranteed. Disney only sells 96% of the points representing all the room-nights they have available, so there's no way for every room to be sold out on average. However, at very high-demand times it can be impossible to get more than a couple nights in a row in a single room. That's a rarity that typically only occurs in the weeks around Christmas and New Years and a few other holidays.
The resort that usually has inventory available all the time is SSR, so if you don't book early enough you may have to settle for SSR. Of course, lots of people like SSR a lot, so it's not "settling" if you love it.
What most people do is make a booking at 11 months in advance at their home resort so they have something for sure, then at 7 months they see if they can move to another resort. As it gets closer and closer to the arrival date, it becomes harder to get what you want. For the really high-demand resorts, they can get completely booked solid by 5 or 6 months out. People do cancel on a regular basis and there is a waitlist, so you can go ahead and wait list a room at the resort you want, and it might get filled all the way up to 7 days before arrival.
For most resorts, most of the time, you can get whatever you want at 11 months at your home resort, except for a few room categories that have very few rooms, most notably Value and Club rooms at AKV.
At 7 months, you can get most room types at most resorts, but some of the most popular room types can be tough to get long contiguous bookings. Those include:
- Grand Villas anywhere but SSR
- Standard and Boardwalk view at BWV, especially Studios
- "Near hospitality house" rooms at OKW
- Standard view at BLT
- Value and Club rooms at AKV
In general, Studios and Grand Villas sell out first; Studios because they're efficient uses of points and Grand Villas because there aren't very many of them.
One-bedrooms are the last to sell out, because they cost twice as much as Studios but sleep the same number (except at BLT and AKV Kidani where they sleep 5). Two-bedrooms are in between One-bedrooms and Studios as far as speed to sell out.
What is the process for reserving a room? Do I actually call Disney and book the room with my points?
You can do that, or there is an online site where you can make reservations. Complex reservation changes need to be done on the phone. "Complex" means anything more complicated than canceling an entire existing booking and making a new one. For example, adding a day or subtracting a day or making a new reservation while keeping your old one held until the new one is confirmed is something you can't do online; you need to use the phone.