First and foremost: If there is a warranty or you know the builder then follow their recommendations for warranty purposes.
Now you will obviously get many different responses about this, this is just from my experience (building anything from 800 hp n/a LS motors to 1st gen small blocks and diesels) and discussions with some of the best builders out there. After most rebuilds, there are generally at most 3 or 4 reasons for a "break in" period.
If it has a flat tappet cam, then the cam and lifters need to "break in" together. This is done after priming oil system (as stated already, use a dino oil with zinc additives or an actual break in oil). Fire up engine, set timing and run for ~20 min between 2000 and 2500 rpms. If running a roller cam then no cam break in is necessary.
Next is Seating the rings. This is very important for a good running, powerful engine. The rings need to seat to the cylinder walls or you could have low compression, excessive blow by, oil consumtion etc. There is somewhat of a window for this to happen. As the engine heat cycles over and over the walls of the cylinder will harden and if the rings haven't seated properly by this time your stuck with it. Now if your carb is dumping too much fuel then cyl walls will get washed down and the rings will not seat properly. The key to seating rings is cylinder pressure, you need to push the rings out against the cylinder wall for them to seat, you get cylinder pressure by loading the engine.
Something else that may need to be broken in is the valve springs. This depends on the spring and manufacturer, but some springs need to be heat cycled to finish treating them. This is done per manufacturer specs but usually just requires warming up the engine and letting it cool completely a couple times prior to beating on them.
The final reason for break in is to wash any leftover crap out of the engine and into the pan.
My typical break in procedure: Double check everything, fill with break in oil, fire motor and get timing close (if distributor, if injected I'll make a start up tune), if it is a flat tappet cam I'll run it through the procedure above. If not, I'll just warm the motor up and check for leaks then let cool. Repeat heat cycle at least one more time. Change oil and check filter for anything alarming, sticking with break in oil. At this point (assuming no engine dyno, and engine in vehicle) I would tune the engine's idle and part throttle fueling and timing, carb or injection. After that, strap it on the dyno and start making pulls (No better way to get cyl pressure than full throttle pulls on a dyno!
) . When done tuning, drive it like you stole it. Change oil at 500 miles and inspect, refill with your favorite oil and be on your way.
Obviously there are many different types of engines and components out there which is why the builder should always be consulted. This is just my .02
-Kyle