This depends greatly on your overall purpose. There are a number of points, probably in the 50-80 range that are used fairly often, and then quite a few more that are for more particular cases (i.e. certain medical conditions that you won't see too often), and then quite a few more that you might use given a particular style of acupuncture, and yet more than you may never use.
Even though this is repeated many times on the site, acupuncture is -not- a point to condition modality generally speaking. Using it that way instead of with appropriate point combinations, which requires a deeper understanding of the underlying theory, will lead to inferior results. Tuina and other "professional" system of acupressure like Shiatsu, require a fair amount of training when compared to learning for self-help. You need to know which points you are using, which meridians you are using, and why - exactly. Otherwise you are just moving things around and this cannot possibly help people and runs the risk of making their conditions worse.
I have an article of very commonly used acupressure points, which for the lay person would be all you need to know for the most part. These could easily be worked into a general bodywork session with little understanding. Because of their broad functions they are part of the small subset of points that can be used on a point-to-condition framework with minimal risk.
As for point memorization, you should start by memorizing the paths of all of the meridians. You should be able to draw them on a paper body - and as a bodyworker this is more important than the individual points. Then on each meridians find some of the most commonly used points and start memorizing them. Within our charts there are a few helpful tools for students that sometimes go unnoticed. First when you are looking at a particular meridian graphic, say the Heart Meridian, you can hold your mouse over any of the points and the location and any precautions will popup (it may work better with firefox instead of internet explorer as your web browser). Second, when viewing a particular point page, like HT 7, you can click on the "Actions and Effects" link which will take you to a chart with all the most necessary points on that meridian and their effects. For acupressure, you probably only need the ones with longer descriptions - so on the heart meridian (HT 5 and HT 7).
After you get the meridian paths and the main points down you want to have some basic understanding of how to use them appropriately. To start you should read my article on basic acupuncture point selection. This will give you a broad framework within which to choose points. After that you should get into more basic diagnostic criteria - which would be most common organ patterns as listed in the TCM theory section. After you get a handle on all of that and have the basic points and patterns memorized you should be well on your way.
To go further you could continue by reading the acupuncture point categories page and clicking on each of the "detailed theory" links next to each category. This will take you a little further into TCM theory and help with appropriate point selection.