Will I need the Spycraft core book to make heads or tails of the material in Shadowforce Archer? [/B]
No. The few bits that are a little different are all covered in the
Spycraft Lite free .pdf you can download at the site (
www.SpycraftRPG.com). The class descriptions and first five levels of each psion class are also posted for easy browsing (In the SFA page's preview material), so you can check out quite a bit of it right now.
The essentials are there are three types of psionic characters: Mentalists, Physical Adepts, and Telepaths. Each has a 20-level base class associated with it (in Spycraft you can start out as a psion if you like). Once you've taken at least one level in one of those classes, you can start taking feats associated with that class. Each of these groups of feats includes three "Basics" feats that let you start spending skill points on several psionic powers (they make all psion skills of that type class skills for that character). Each psion skill generaly has three things you can do with it (powers). So, you get...
Mentalist
Psychoinventive Basics (Focus the Mind, Gadgeteer, Static Charge)
Psychokinesis Basics (Cryokinesis, Photokinesis, Pyrokinesis)
Telekinetic Basics (Kinetic Shield, Levitation, Poltergeist)
Physical Adept
Adrenal Basics (Body Sculpting, Energy Burst, Speed Control)
Metabolic Basics (Control Metabolism, Control Pheromones, Pain Transmission)
Sensory Basics (Combat Sense, Enhanced Senses, Extended Visual Spectrum)
Telepath
ESP Basics (Clairsentience, Empathy, Psychometry)
Imprint Basics (Dominion, Project Thought, Telempathy)
Intuition Basics (Catalyst, Precognition, Synthesis)
There's also feats that let you improve your mastery of one type of psionic power, some that could be likened to meta-magic for your powers, and some that are for high level characters that are just plain scarry (but take lots of work). For example if you have the feat Telekinetic Mastery, you can wrap your TK Shield (generated by making a skill check with the Telekintetic Shield psion skill) around an ally instead of yourself.
The Archer Foundation adds 9 more psion skills (one for each 'basics'), a prestige class for each type of psion, and a colection of new psion feats if you like what you see in the SFA worldbook

.
Hope this helps,