A suggested first step is to visit a nearby smaller airport and inquire about a "Discovery Flight" or "Introductory Flight".
Most flight schools offer these which will include a brief first lesson with a Certificated Flight Instructor ("CFI") where you will sit in the pilot's seat and get to handle the flight controls - typically when 1,000' or more above the ground.
This will introduce you to flying with no commitment. If there is more than one flight school near you, you will want to visit each of them to get a good idea of how they conduct business and decide if they meet your expectations. Some schools are better, friendlier or more modern than others and you can determine if a slightly more expensive school may or may not be worth it.
Student Pilot Certificate and Third Class Medical Certificate (Required to 'solo', or fly by yourself)
Previously this was issued as a combined "Student Pilot Certificate / Third Class Medical Certificate" by an Aviation Medical Examiner.
But now, the Student Certificate is a separate document issued by the FAA. Your CFI will help you get this, but it isn't required until you are ready to solo.
The Third Class Medical Certificate is issued by an Aviation Medical Examiner. Like the Student Pilot Certificate, this isn't required until you are ready to solo.
This is a fairly simple medical exam. The medical is valid for 5 years / 60 months if obtained when under 40 years old, 24 months if issued when 40 or older. See the "Basic Med" information and links under Private Pilot below.
Flight instruction can be received at any age, but to solo an airplane, you must be 16 years old.
Gliders and balloons can be soloed at age 14.
The Student Pilot's logbook is signed by a Certificated Flight Instructor ("CFI") to allow you to solo, and later, to take solo cross-country flights.
No minimum hours are specified, but details of training required are spelled out in Federal Aviation Regulations ("FARs") 61.81 thru 61.95. Most pilots can solo in about 10 hours, but this is widely variable.
Passengers may NEVER be carried by a Student Pilot.
The Private Pilot certificate is usually what is referred to when discussing getting a "pilot's license".
Minimum age - 17
Allows carrying of passengers in relatively good weather - Visual Flight Rules ("VFR") both day and night.
Third Class medical required. (Same duration as for Student Pilots listed above). As of May 1, 2017: Changes to the regulations allow many operations under "Basic Med". More detail here.
Specified flight training, solo and solo cross-country experience, a "Knowledge Test" and written recommendation from a CFI is required prior to taking the Practical Test (an Oral and Flight Test) from a Designated Pilot Examiner.
Either of two possible sets of rules can be used to get your Private Pilot's License: either FAR Part 141 - at an "FAA Approved" Flight school, or FAR Part 61
FAR Part 61 Minimum flight experience (full list is in FAR 61.109)
40 hours total flight time
20 hours dual instruction ('dual' is flight time with an instructor)
3 hours night, including 10 night takeoffs and landings and a 100 nautical mile night flight.
10 hours solo, of which 5 hours is solo cross-country, including one 150 nautical mile cross-country solo flight.
FAR Part 141 allows some ground simulator time to be applied toward the certificate and has different requirements.
40 hours of simulated instrument time under the 'hood' - which is flying with an instructor while you wear a 'view-limiting device' allowing you to only see the instruments.
FAR 141 generally requires fewer hours.
Another Knowledge Test and Practical Test is required.
There are provisions for an ATP with restricted privileges with 1,000 hours if a Bachelor's degree graduate from certain universities. (See FAR 61.160)
Required certificate to be a Captain for an airline.
Previously this was not required by the FAA to be a Copilot / First Officer for an airline, but now at least a Restricted ATP is. Details can be read here: Restricted ATP
A First Class Medical is required. The medical is valid for 12 months if obtained when under 40 years old, 6 months if issued when 40 or older
(for ATP privileges).
Another Knowledge Test and Practical Test is required.