Before you take delivery, examine all the aircraft paperwork thoroughly. Being told that "the flight manual will be delivered later" or that "the airworthiness certificate is in the mail" will not satisfy the FAA - and it shouldn't satisfy you because you are the one the FAA will violate if it discovers that those required documents are not in the aircraft.
When you take delivery of your new airplane, don't assume the manufacturer has completed a thorough pre-delivery inspection - especially if you pick the aircraft up at the manufacturer's facility. Naturally, the manufacturer has inspected it, but that doesn't mean the inspector hasn't missed something. I have ferried many new aircraft from several companies, and it wasn't at all unusual for me to find discrepancies. This includes airworthiness items such as missing exterior inspection panels, improperly rigged controls, etc.
As is always the case in aviation, the primary mission is safety. A pilot should always be prepared for the worst-case scenario. This is especially important when breaking in a new aircraft. After you're satisfied that your new airplane is airworthy, you should pay close attention to a number of things during its first hundred or so hours of operation. Some are safety of flight items and others are those you should check while the manufacturer's warranty is in full effect.
Obviously, the engine is an important component that you need to monitor - and operate - carefully. Though it's an extremely rare occurrence, new engines do fail. It may not be the engine that fails but some engine accessory such as the carburetor or fuel injector unit, gascolator, or the fuel selector valve. Regardless of what fails, the result is the same - a partial or total loss of power. Pilots should not be complacent just because they have a brand new airplane.
During its first hours be sure to operate your engine exactly as the manufacturer recommends. It's a mistake to think that during the break-in period, you're "saving" the engine by using partial power for takeoff and other phases of flight. In fact, you'd be hurting it because the engine isn't developing the rpm, heat, and pressure needed to seat new piston rings and valves, and break in other components and systems. So if the break-in procedure calls for cruising at 75 percent power or more during the first so many hours, do the engine (and yourself) a favor and give it what it needs.
If you plan to fly high in your new airplane, be careful how you reduce power. Shock cooling the cylinders will probably reduce engine life significantly. Reduce power slowly from the cruise setting. Don't ruin your engine by agreeing to ATC requests for rapid descents from altitude. A bit of planning generally provides for a smooth descent at gradually reduced power levels.
Be sure to follow the manufacturer's recommendations regarding the type and weight of oil and filter (if any) to use during break in, and change the oil at the stated intervals. Monitor the engine oil level closely and keep track of your engine's actual oil consumption. It will probably be fairly high for a short time and then drop off significantly. If it remains high beyond the first 100 hours, you probably have either a messy leak or piston rings that have not seated. If your rings have not fully seated by the first 100 hours, they probably never will.
Check your spark plugs several times during the first 100 hours of engine operation. Often, new engines are run with richer than normal mixtures, which means lead deposits can build up quickly. Have your maintenance technician recheck the mixture setting and the ignition timing after the first 100 hours or so and reset them, as necessary, to the correct settings.
Engines and airplanes vibrate, so after the first 10 hours, make a complete under-the-cowling check for mechanical integrity of the engine and its controls, hoses, belts, fasteners, etc. Repeat this check at 25-hour intervals for the first 100 hours or so.
During the first 100 hours you should operate all of the aircraft's mechanical, hydraulic, and electrical equipment as often as practicable. Any significant mechanical, hydraulic, or electrical problems rooted in the original manufacturing of the aircraft and its equipment will most likely show themselves in that time if you give them the opportunity.
Turn on all the avionics equipment on every flight. This allows you to check all the calibrations, program all the systems, check all the indicators and panel lights, and use all the navigation, communications, and intercom systems to find out what does and does not work properly while the equipment is still under warranty. Letting a warranty expire without doing everything possible to uncover a malfunction can be expensive.
On the airframe, check all moveable control devices for play and proper adjustment. The flight controls should be free but should not have play in the hinges.
When the yoke or stick is in the neutral or centered position, the ailerons should line up together with the wing trailing edge, and the elevator should line up with the horizontal stabilizer. When you move the yoke, the appropriate control surface should begin to move immediately. The rudder should be free, line up with the vertical stabilizer when the rudder pedals are centered, and begin to move as soon as you depress a pedal. Slack rudder cables are a common problem in many general aviation aircraft. Trim tabs should feel solid on their mountings and begin to move as soon as you move the trim control.
Be sure to check frequently for proper tire inflation. Improper (especially low) tire inflation is the primary cause of rapid tire wear and can be a safety hazard as well. Even a slow leak in a tire or tube will become apparent early on if you're looking for it. Check your brakes immediately after engine start and frequently thereafter to ensure that they function properly and that they "burn in" properly. Don't "baby" the brakes. Apply them heavily early in the game to seat and wear in the pads or shoes properly.
Finally, every time you look at your new pride and joy, examine it closely for loose and missing fasteners, loose rivets, chipped and cracked paint, and cracked plastic parts. Fasteners come loose and may be missing on any aircraft regardless of age. Chipped or cracked paint might indicate parts that shouldn't be are moving relative to each other. It can also indicate that joints between parts intended to move relative to each other were incorrectly painted over. Plastic parts on aircraft are not without their problems, such as cracking.
Breaking in an airplane entails specific procedures and operating requirements, but the result is worth the effort to learn and follow the manufacturer's break-in recommendations. If you give your new airplane the best possible start in life, and if you take care of it, it will take care of you.