This web site for the US Passport Office has all of the information you need, including the passport application that you can print and submit. http://travel.state.gov/passport/passport_1738.html
The process in simple terms:
-Print off the passport application from the web site above.
-Have two passport photos taken; at many travel agencies or an AAA office.
Submit/mail your application to the Passport office along with the required 2 photos and the application fee of $100 for an adult passport, include an original or certified copy of your birth certificate.
Processing takes about 4 weeks. You can request and pay for expedited service of about a week; its explained on the web site.
Differences:
The passport card is $45 vs $100 for a passport book.
The Passport card is good for land border crossing between the US, Canada, and Mexico and sea cruise border crossings in the Caribbean and Bermuda. The passport is acceptable everywhere.
Both are good for 10 years; the passport renews for $75, the passport card for $20 : http://travel.state.gov/pdf/ppt_pptCard.pdf
Regardless of which you apply for you will still have to submit the exact same documentation; photos, proof of citizenship and proof of identity. SO the bottom line is which is more convenient and conveniently priced for you.