As you've probably figured out, certifications don't "expire," so "re-certification" is probably not the best term to describe what takes place.
In the simplest terms, a pilot certificate is issued for life unless it is revoked or suspended. The certificate is not the only thing required to operate as a pilot though. Medical certification and recent experience are the keys to determining eligibility to operate as a pilot.
Medical certificates do expire, on intervals of 6 months, 2 years, or 5 years depending on the level of certification held. The most strict type, a Class 1 medical certificate, is held by Part 121 pilots and must be renewed every 6 months.
The minimum experience to fly as a solo pilot would be a biennial flight review, required to be one hour of flight and one hour of ground instruction performed by a certified flight instructor, to be completed by the end of the 24th month following the last one. In practice, it's more legal than safe to avoid flying for 23 months and then jump back into the saddle solo. To fly with passengers or at night, there are more recent requirements.
To fly in the clouds or over 18,000ft, an instrument rating must be added to the pilot certificate. This does not "expire," either, but requires much more recent experience to be exercised. Again in general terms, one must shoot 6 instrument approaches (actual or simulated) within 6 months, or complete an instrument proficiency check with an instructor within 12 months.
These regulations are generally explained in the Federal Aviation Regulations (FARs), parts 61 and 91. These are aircraft and aircrew certifications and operational requirements in general terms. More complex operations, such as charter and regularly scheduled airline service, have their own FARs. Parts 135 and 121 apply to these kinds of operations.
One major difference between "vanilla" Part 91 operations and Parts 135 and 121 is the existence and approval of operating procedures. Each airline or charter operation produces their own procedures which are then reviewed and approved by the FAA. These procedures are likely to include much more stringent recent experience, training, certification, and similar requirements that the entire operation and each of its pilots must follow. They are modeled after the FARs, but can be structured to the types of flying pertaining to the particular operation.
A lot of examples of operational procedures, the complete FARs, and anecdotes about all of them can be found on the web.
Position and hold