Student Pilot Requirements:
There are no requirements to start taking lessons, except proof of citizenship or TSA authorization. At about half way through your training, when you're ready to fly the airplane by yourself for the first time, known as "solo," you do need to be at least 16 years old (No maximum age) and pass a 3rd Class medical exam, administered by an FAA designated physician or AME, which also serves as a student pilot license.
You will also need to get the necessary flight and ground training and pass a pre-solo knowledge exam prepared by your instructor. When your instructor feels you're ready to solo, (10 consistent takeoff and landings without intervention) he or she will endorse your logbook and student pilot certificate. Then you can fly by yourself in the local area, though you won't be able to carry passengers until you finish your private license, 
Private Pilot Requirements:
Eligibility requirements: FAR §61.103  
General,
To be eligible for a private pilot certificate, a person must:
(a) Be at least 17 years of age for a rating in other than a glider or balloon.
(b) Be at least 16 years of age for a rating in a glider or balloon.
(c) Be able to read, speak, write, and understand the English language. If the applicant is unable to meet one of these requirements due to medical reasons, then the Administrator may place such operating limitations on that applicant's pilot certificate as are necessary for the safe operation of the aircraft.
(d) Receive a logbook endorsement from an authorized instructor who:
(1) Conducted the training or reviewed the person's home study on the aeronautical knowledge areas listed in §61.105(b) of this part that apply to the aircraft rating sought (such as studying the Gleim Private Pilot FAA Knowledge TestGleim Private Pilot Flight Maneuvers and Practical Test Prep, and Gleim Pilot Handbook).and
(2) Certified that the person is prepared for the required knowledge test.
(e) Pass the required knowledge test on the aeronautical knowledge areas listed in §61.105(b) of this part.
(f) Receive flight training and a logbook endorsement from an authorized instructor who:
(1) Conducted the training in the areas of operation listed in §61.107(b) of this part that apply to the aircraft rating sought; and
(2) Certified that the person is prepared for the required practical test.
(g) Meet the aeronautical experience requirements of this part that apply to the aircraft rating sought before applying for the practical test.
(h) Pass a practical test on the areas of operation listed in §61.107(b) of this part that apply to the aircraft rating sought.
(i) Comply with the appropriate sections of this part that apply to the aircraft category and class rating sought.
(j) Hold a U.S. student pilot certificate, sport pilot certificate, or recreational pilot certificate.
Private Pilot Privileges and Limitations:
As a private pilot, you may not act as a pilot in command of an aircraft that is carrying passengers or property for compensation or hire, nor may you be paid to act as a pilot in command, 
Except: 
You may act as a pilot in command, for compensation or hire, of an aircraft in connection with any business or employment if the flight is only incidental to that business or employment and the aircraft does not carry passengers or property for compensation or hire.
You may equally share the operating expenses of a flight with passengers, provided the expenses only involve fuel, oil, airport expenditures, or airplane rental fees.
If you are an aircraft salesperson and have at least 200 hr. of logged flight time, you may demonstrate an airplane in flight to a prospective buyer.
You may act as a pilot in command of a charitable, nonprofit, or community event flight described in 91.146, if the sponsor and pilot comply with the requirements of91.146.
You may be reimbursed for aircraft operating expenses that are directly related to search and location operations, provided the expenses involve only fuel, oil, airport expenditures, or rental fees, and the operation is sanctioned and under the direction and control of a local, State, or Federal agency; or an organization that conducts search and location operations.

Free FAA Reference: 
Airplane Flying Handbook
Pilots Handbook of Aeronautical knowledge
Aeronautical Information Manual
Practical Test Standards 
Federal Aviation Regulations
How to get a good Weather Briefing
AOPA Weather Briefing
Sample FAA Private Pilot Knowledge Test

Additional Study
Private/Recreational

FAR
Part 1
1.1
1.2
Part 21
21.181
Part 39
39.3
Part 43
ALL
Part 61
61.3
61.15
61.23
61.31
61.56
61.57
61.60
61.69
61.95
61.101
61.113
Part 71
71.5
71.71
Part 91
91.3
91.7
91.9
91.15
91.17
91.103

91.105
91.107
91.111
91.113
91.115
91.117
91.119
91.121
91.123
91.125
91.126
91.127
91.129
91.130
91.131
91.135
91.151
91.155
91.157
91.159
91.203
91.205
91.207
91.209
91.211
91.215
91.303
91.307
91.309
91.313
91.319
91.403

91.405
91.407
91.409
91.413
91.417
NTSB
830.5
830.10
830.15
AIM
Chapter 1
1-1-4
1-1-17
1-1-18
Chapter 2
2-1-2
2-1-7
2-1-8
2-1-9
2-3-3
2-3-5
2-3-8
2-3-11
Chapter 3
3-1-4
3-2-1
3-2-3
3-2-4
3-2-5
3-2-6
3-4-3
3-4-4

3-4-5
3-4-6
3-5-1
3-5-2
3-5-4
3-5-5
Chapter 4
4-1-8
4-1-9
4-1-11
4-1-13
4-1-15
4-1-18
4-1-20
4-2-3
4-2-9
4-2-13
4-3-3
4-3-4
4-3-10
4-3-11
4-3-14
4-3-18
4-3-23
4-4-6
4-4-15
Chapter 5
5-1-4
5-1-13
5-1-14
5-2-4

Chapter 6
6-2-4
Chapter 7
7-1-3
7-1-4
7-1-5
7-1-8
7-1-10
7-3-2
7-3-3
7-3-4
7-3-5
7-3-6
7-4-6
Chapter 8
8-1-2
8-1-3
8-1-4
8-1-5
8-1-6
8-1-8
Pilot/Controller
Glossary