Power points are spent to augment the Psion's at-will powers. Each Psion at-will power has the keyword augmentable, and a number of additional clauses in the text that tell you what to do based on how many points you spend to use the power. By default the expenditure is 0.
As far as a list of powers for Psions, your best bet is the Wizards DDI compendium. Even if you are not a subscriber the search functionality is quite helpful to find the source locations for each power and for creating lists of things (for instance you can filter the entire powers list to Psion, At-Wills). There is also the Psion Char-Op Guide, which as with all the Char-Op guides is recommended reading and has a complete list of power selections and some helpful strategies for building a character.
Psions do not get a spell book, they get powers just like everyone else, the spellbook is a uniquely wizard exception. They do not get regular encounter powers, just At-Wills, Utilities and Dailies. Psions can and do take feats to give them ritual caster abilities that are contained in a ritual book, but that's neither here nor there with respect to power points.
Just so it's perfectly clear, Psions trade their encounter powers for encounter renewing power points which effectively model and follow an incredibly similar progression to regular AEDU class encounter powers. There is no real change in the power balance structure here.