You must pass a written examination on private pilot aeronautical knowledge.
The following is a Private Pilot Test guide by the FAA. This link also provides a few sample questions and a description of the exam.
http://www.faa.gov/training_testing/testing/test_guides/media/FAA-G-8082-17I.pdf
The private pilot aeronautical knowledge required is described in 14 C.F.R § 61.105.
The following link has the FAA Question bank to study with. You can thank the Freedom of Information Act for this information being publically available.
http://www.faa.gov/training_testing/testing/test_questions/media/pvt.pdf
There are many great test guides out there to help study with; however, I am personally a big fan of Gleim. Prepware and Jeppesen also have great guides. These guides provide the questions, the answers, and a brief explanation of the answer. Typically the Gleim book is around $20.

This test consists of a 60 questions. You are given 2 1/2 hours to complete the test. A score of 70% or better is required to pass.
You can take practice exams at www.exams4pilots.org. Just make sure to select the right exam, and the right number of questions. A lot of times, your instructor might ask you to take this test over and over again, and when you can consistently take and show a high passing grade, he will endorse you to take the real written.
I personally recommend taking the written exam as early as possible. This will allow you to find weak areas, and help gain a better understanding before the oral exam and checkride. Often, students will end up completing all of their training and end up having to wait on taking their written.
You must pass an oral examination with a Designated Pilot Examiner
This is typically done with the DPE as part of the Checkride. This might include questions similar to what was on the written exam, especially questions on the topics you missed. It might also include a discussion of various emergency scenarios and what you would do. Then it might conclude with a discussion of your flight plan, why you chose the route you did, and a discussion of various airspace and obstacles along your route.
ASA has great oral exams guides that consist of sample questions and answers. This book might be around $15

You must pass a practical examination (also known as Checkride) with a Designated Pilot Examiner.
This is essentially the “drivers test.” This is where you and the examiner go flying and you get tested on all the required maneuvers. The FAA has published what is known as the “Practical Test Standards (PTS).” This is essentially a checklist of everything that is expected of you and the examiner on your Checkride. This is published so there are no surprises on your flight. This contains all the requirements and what standards you must meet to pass.
http://www.faa.gov/training_testing/testing/test_standards/media/FAA-S-8081-14B.pdf
It is a very wise idea to completely read through this before your Checkride and possibly along with your flight instructor.
As you can tell, this particular item is available online for free in the link above; however, ASA prints this in a small book form too. This is typically about $5.
