The brief answer is that you learn it the same way as anything else,
which is to break the process down into manageable small elements.
Start by recognizing that you are unlikely to need all the possible
capabilities of the program at the outset. This makes it much
simpler to make headway. Next decide on the three or four tasks
that are of the most interest to you at the beginning. For instance,
do you primarily want to enhance and print photos, or create web
graphics, or do digital arts and crafts projects, etc.?

Once you've established these things, you can move to the various
learning resources. Included with the program (under Help) is a
Product Tour and a Learning Center. These give some idea how to set
about various tasks. The Help system, in contrast, is not task
oriented but instead explains how to use the various controls.
The Learning Center (http://www.jasc.com/support/learn/?) on the
Jasc web site includes projects and introductory materials here:
http://www.jasc.com/support/learn/psptutorials.asp? Additionally
the PSP FAQ (http://campratty.com/questions.html, and also
http://campratty.com/index.html and http://campratty.com/search.html)
provides a wealth of information. Another source of help and advice
are the Jasc User Forums (http://www.jasc.com/community/forums/?).

When you have a little basic familiarity with the program and its
tools, you can move onto accomplishing specific projects, for which
many tutorials are available. One of the most extensive listings
of PSP tutorials is here: http://www.psplinks.com. Should you run
into trouble with a tutorial or fail to understand it, I would
recommend asking a question about it in the Forums. The people
there are very helpful. Once you know enough about the program to
know what you don't know but would like to know, you could also
consider taking an on-line class. One particular one that has been
popular with people is http://www.lvsonline.com/. Courses are
offered on PSP 8 (http://www.lvsonline.com/courses1a.shtml) and
on PSP 7 (http://www.lvsonline.com/courses1a.shtml#psp7) and are
geared to various levels of expertise and to different interests.
Depending on your particular interests, there are also newsgroups
devoted to specific aspects of PSP such as tubes or scrapbooking.
A number can be found on the news.annexcafe.com server.

I hope this has given you an overview of where you can find learning
information. You will discover that PSP users are a helpful lot,
who are very willing to assist a beginner. If you do ask questions,
though, please try and make them as specific as possible since that
usually generates the most useful replies.