Maintenance in the US runs on a few parts of the Federal Aviation Regulations (14 CFR): part 43 (how maintenance is done and recorded), part 65 (mechanic certificates), part 91 (owner and operator duties, including inspections and records) and part 39 (airworthiness directives).
Data to work from
Work must follow the manufacturer's manuals or other acceptable methods. AC 43.13-1B gives acceptable methods for many minor repairs when the manufacturer doesn't say otherwise. A major repair or alteration needs approved data: for example the manufacturer's structural repair manual, a Supplemental Type Certificate (STC), an airworthiness directive, or data the FAA approves for that job. The Type Certificate Data Sheet (TCDS) describes how the aircraft was certificated: engines, propellers, limits and equipment.
Airworthiness directives (ADs) are mandatory: the FAA issues them when it finds an unsafe condition. A manufacturer's service bulletin is a recommendation; it isn't mandatory for a part 91 owner unless an AD (or an operator's own approved program) requires it.
Writing it down
A maintenance record entry (14 CFR 43.9) has: a description of the work (or a reference to the data used), the date it was finished, the name of the person who did it, and if the aircraft is approved for return to service, that person's signature, certificate number and kind of certificate. A major repair or major alteration is also written up on FAA Form 337: one copy to the owner and one to the FAA within 48 hours.
The owner keeps the records of routine work until it is repeated or superseded, or for a year. Some records stay with the aircraft for life and go with it when it's sold: total time in service, the status of life-limited parts, time since overhaul, the current inspection status, the status of ADs, and current major alterations.
Human factors: the Dirty Dozen
Twelve conditions that lead to maintenance mistakes: lack of communication, complacency, lack of knowledge, distraction, lack of teamwork, fatigue, lack of resources, pressure, lack of assertiveness, stress, lack of awareness and norms ("we always do it this way"). Each has a counter: write it down, check your work, use the manual, finish the step before stopping, speak up.