An aircraft which conforms to its "type certificate data sheet" and is "in a condition for safe operation,” is considered to be "airworthy" (the FAA only recently defined this condition clearly). The definition of airworthiness is on board every certified airplane on the standard airworthiness certificate but also found in FAA Advisory Circulars AC 43.13-1B and AC 120-77 (both mechanic's guides to acceptable repair techniques). This pdf from 8083-30 (Maintenance Handbook) is a thorough regulatory overview. Notice though that the first element, the data sheet is very black and white but the second requirement is fairly subjective. Your inspection before flight can discover defects that render your aircraft "unairworthy" (in fact anything not working causes this!) Certain actions that you then perform, as a pilot, may then restore this plane to an airworthy condition suitable for "safe operation." It is required that every pilot know these requirements and actions. AOPA has a useful website archive on airworthiness [HERE].
The type certificate is the engineering standard upon which the aircraft was originally certified and manufactured. This document contains the required equipment and limitations that are often stated in the Airplane Flight Manual or Pilot's Operating Handbook. My ancient 1946 7AC "Champ" (TCDS A-759) represents the original type certificate upon which the whole line of Champion aircraft were built. The modern "Super Decathlon" is manufactured under the same ancient TCDS simply modified through the years! Similarly, the entire Mooney line is similarly built entirely on the original wooden tail Mooney of the CAR 3 standard. The CAR or "Civil Aviation Regulations,"before 1958, pre-dated the current CFRs. All subsequent Mooney models were created by Supplemental Type Certificates (modifications of the original design.) Using this older standard allows a manufacturer a greater latitude than certifying an aircraft under the modern, more restrictive, CFR part 23 (amendment 17) aircraft certification. Here is a good article on aircraft categories: [click]
If something is added subsequent to the original manufacture of the aircraft (either by the manufacturer or a private engineering firm) an "STC" (Supplemental Type Certificate) may be used to accomplish this change legally. An STC is basically a new engineering standard and associated data to approve certain modifications to a specified make and model aircraft. An STC is issued under Subpart E of Title 14 of the Code of Federal Regulations part 21. Section 21.113 states, in part, that: “Any person who alters a product by introducing a major change in type design, not great enough to require a new application for a type certificate under section 21.19, shall apply to the Administrator for a supplemental type certificate….” A common STC might be the addition of a new engine or prop or the use of automotive fuel in an aircraft. The STC documentation must "prove" this modification was done legally and "in an airworthy fashion." This means the mechanic followed the accepted data for correct installation and you purchased the STC (and theoretically deferred some of the engineering costs). Usually a Form 337 was also filed with the FAA for major repair and modification of the aircraft. The 337s become part of the aircraft's record and can be purchased from the FAA. Interestingly some STCs, such as using auto fuel, might void your manufacturer’s warranty. More detail on these subjects can be found in a good article by Steven Ells called "Making Modifications." A certificated pilot and owner/operator is legal to make 32 minor repairs under CFR 43.3, Appendix A, Paragraph C: "Preventative Maintenance." Here is an excellent site for some guidance on these regulations: [click]
So, an older aircraft may have quite an extensive file to assure "airworthiness." There is also further verification necessary to "prove" the aircraft continues to meet the original standard. You will be required on your flight test to demonstrate both the airworthiness of your aircraft and your knowledge of this subject on your flight test! Once a year most aircraft must undergo an "annual" inspection to assure that it is in an airworthy condition. This inspection is performed by either a certified repair station or an Airframe and Power plant mechanic holding "inspection authority." This is where the term A&P/IA you might have encountered comes from. Please check your logbooks for the record of this inspection. Be familiar with the required terminology for this sign-off to be legal. If your aircraft is flown for hire or used for instruction it will require a "100-Hour inspection." This is almost the same physical inspections an annual but without the data search for airworthiness directives and certain annually occurring items. This inspection may be performed by an A&P. There are many more inspections that may be required depending on the amount of equipment installed. Orlando FSDO publishes a handy list to check for required inspections. Find and verify the inspections for your aircraft in the aircraft's logbooks.
When you preflight your aircraft hopefully everything is operational. If anything is inoperative your aircraft instantly becomes "unairworthy." Everything must work according to the FAA to be airworthy! Thankfully, there is a simple process by which a pilot can usually "properly alter" an aircraft that has inoperative equipment. This is covered in AC 91-67. Basically, a pilot must determine from the Aircraft Flight Manual and/or Pilot Operating Handbook, if the inoperative item is "required." It may be the AFM/POH or an AD or numerous other imperatives that requires an instrument be operational. If the instrument or equipment is required it must be repaired before flight. "Non-required" items may be "properly altered" and the aircraft then legally flown. This process is outlined in CFR 14, 91.213(d) and basically involves deactivating or removing the offending item, placarding it "inoperative" and making a maintenance notation in the appropriate record. Some items may be repaired by a pilot under CFR 23 "preventative maintenance." Some items will require a qualified mechanic to either repair or deactivate. Ultimately, the plane must be legal and the pilot must also be comfortable with the level of airworthiness. To explain this personal "test" here is an example: Flight at night without an attitude indicator is legal but probably not safe or smart! Flight around the pattern on a sunny, calm day could be easily and safely accomplished even if the fuel gauges were inoperative provided you just filled the tanks...but it would definitely not be legal. So there is always a three-part test: "is it legal, is it safe, is it smart?" The dynamic interface between the pilot, the plane and the planned flight determine the safety of flight.
For your flight test, the best preparation is to envision yourself walking into the FBO and renting the aircraft you intend to fly. Without ever seeing this aircraft before, how would you know positively that this aircraft was "airworthy?" What data would you need? This is what your examiner will require from you on test day. Hopefully, you will later be doing exactly this when you enter an FBO on vacation somewhere and want to rent an aircraft. You must positively verify the airworthiness of your rental. This would include logbooks with the most recent inspections for annual, 100 hour, transponder, ELT etc. Depending on the complexity of your aircraft you might have quite a file. For your test day, what you want to demonstrate to your evaluator that first, the aircraft you are flying for the test is indeed airworthy, and second, you personally know how to analyze and decipher maintenance entries to insure this is true. Marking the various entries with tabs or post-it notes saves time and demonstrates good organization to your examiner! (Did you also remember to calculate the weight and balance and the take-off and landing performance?)
If you own a private aircraft and hire a flight instructor you are not subject to 91.409(b) which requires a 100 hour inspection when "flown for hire." It is also true that if you fly a club aircraft and hire a CFI you do not need a 100 hour inspection. If however, the club supplies the AIRCRAFT AND CFI for training, a 100 hour inspection is required! Any contractual relationship that recommends, restricts or proscribes "authorized CFIs" would mean the club is also required to do 100 hour inspections. Here is a good article from AOPA and here is the FAA Chief Counsel Opinion on this subject.