Is it possible to use Hilton HHonors points at other hotel affiliated with Hilton? Or, put more generally, what are some strategies on making the most of Hilton HHonors points.
I suspect you're confusing the two different uses of the name "Hilton" - which isn't surprising as it's somewhat confusing!
The two things that are normally referred to as "Hilton" are "Hilton Hotels & Resorts" and "Hilton Worldwide".
Hilton Hotels & Resorts is the full name for the actual "Hilton" branded hotels (Previously they were simply known as "Hilton Hotels").
Hilton Worldwide is the company behind the entire Hilton portfolio of hotels, which includes not only the "Hilton" (ie, Hilton Hotels & Resorts) branded hotels, but also all of their other brand such as Waldorf Astoria, Conrad, Doubletree, Embassy Suites, Hilton Garden Inn, Hampton, Homewood, Home2 and Hilton Grand Vacations.
Hilton's frequent loyalty program, Hilton HHonors, is run by Hilton Worldwide and covers all of their brands - so you can collect points and redeem points at all of the hotels listed above. It's a single program across all brands, so you have one set of points, and one level of status across all of the hotels - although the actual points you earn at each can vary, as do the benefits of status with each.
If you want to use points at a different, non-Hilton Worldwide hotel then you're pretty much out of luck. The only options you're going to have are to transfer the points to something like an airline frequent flyer program, and then transfer them to another hotel chains loyalty program. Even if you can find an intermediate program to use to do that transfer, the cost (either in terms of a fee to do the transfer as well as the number of points you'll lose in the transfer) almost certainly makes it not worth doing.
Some airline programs will allow you to book hotels using points, in which case you could transfer the Hilton points to airline frequent flyer points and book the hotel there, but again the conversation rate probably makes it not worthwhile.
Some programs do allow you to transfer points from one loyalty program to another using websites like points.com, however Hilton do not allow this.
Doc's answer gives you a good introduction, and should get you started. After that, two good resources I know of for HHonors are both on FlyerTalk. I'd suggest you have a read through two sticky threads there: Frequently Asked Questions (FAQs) Pertaining to Hilton HHonors and Making sense of Hilton reward option.
In terms of making best use of the program, assuming you're staying a fair bit in Hilton properties, I'd suggest the following: