First of all, you do not fill out the DS-82 form. That's only for adults that are renewing their passports by mail. You have to fill out the DS-11 form, available here:
http://travel.state.gov/passport/forms/ds11/ds11_842.html
You are correct about going in person. Because you've never gotten a passport before, you have to apply for your first in person. Just so you know, not all post offices do passport stuff. You can search for a location here:
http://iafdb.travel.state.gov/.
The only reason you would want to go to a Passport Agency is because they can get your passport to you more quickly. Here are the locations:
http://travel.state.gov/passport/passport_4312.html
I suggest you pick one that does photos on site. If you don't, you have to get your own photos that are 2" X 2" showing your face. They can also only have a white background. Since the specifications are a little complicated, I find it best to just have it done at the facility. The other place you can get passports is at your Regional Passport Agency, though those are few and far between. Post offices are best.
You must submit evidence of U.S. citizenship. Normally, one would just bring in an old passport. Because you don't have one, you will need to bring one of the following: a certified birth certificate issued by the city, county, or state; a consular report of birth abroad or certification of birth, a naturalization certificate, or a certificate of citizenship. If you are just a regular ole citizen, just bring your birth certificate. Remember, you cannot just photocopy this! You have to get an official copy from your city, county, or states' records office.
You need to present identification. Like you thought, your driver's license is good for this. You also need to submit your social security number. You don't have to have the card or anything, but you have to provide it on the form.
Of course, you need to bring money to pay for the passport. Just so you know, many post offices only accept certain forms of payment. Debit cards, checks, and cash are good, but credit cards may not be acceptable.
Things you need to bring:
1. Completed DS-11 form
2. Birth certificate or one of the others listed above
3. Driver's license
4. Method of payment
5. S
All this info can be found at the U.S. Department of State's website:
http://travel.state.gov/passport/get/first/first_830.html
You also asked what the difference between a passport book and a passport card are. A passport book is the normal blue (in the United State's case) booklet you see when you think of a passport. A passport card is something the government recently started doing. Passport cards are the size of license's and credit cards. The benefit of them is that they are more compact than the passport books. However, you can only use passport cards to travel over land to other countries. Basically, you could drive to Mexico or Canada with one. You cannot use it to fly to those countries, though. Passport books, on the other hand, let you go, by any method, to any other country, unless it's on the list of countries you can't travel to, like Cuba.
Have fun in your travels!