Do a search on this forum for Mahlon Russell's break in procedures. His posts on the topic are pure gold.
Be aware there are TWO different procedures - one should be very careful not to confuse them.
1) RUN IN - this is done with a brand new engine, just assembled. The procedure for run-in includes some very specific instructions on X RPM for Y minutes. If your engine has been built by a reputable shop, this run-in procedure has almost certainly been done for you in a test cell. New factory Lycoming engines have the run in procedure done at the factory.
2) BREAK IN - this is the next stage in the engine's life where we break in the piston rings against the cylinder walls. This is the one where we want to be running either mineral oil or Phillips XC multi-grade (no other multi-grade oil, no Aeroshell multi-grade, no Cam Guard or similar). We're trying to get the friction between piston rings and cylinder walls to wear the two surfaces to the point of making a good seal. Once this is accomplished, temperatures will drop and oil consumption will stabilize. The best way to achieve this break-in seems to be to run at high power settings (nothing below 75%) while keeping the engine as cool as possible. That means FULL RICH mixture, low climb angles for good cooling airflow and staying over the airport in case something in that new engine isn't quite right. Keep your altitude low as climbing to higher altitude will both prolong low cooling airflow and raise density altitude to the point where getting the desired high power setting may not be possible.
With respect to ground runs, Mahlon's advice on that topic is excellent. In a nutshell, perform ground runs as often as is necessary to ensure all systems are functioning properly. Monitor CHT. NEVER let CHT get above 300 degrees F. Do a ground run, shut down before hitting 300F, let the engine cool to the point where you can comfortably rest your hand on the cylinders for 30 seconds. Only when the engine is this cool is it safe to start up and do another ground run, again to a CHT limit of 300F. This advice is critical for preventing glazing of cylinder walls.
I followed Mahlon's recommendations for ground running and breaking in our factory-new O-360. Temperatures stabilized in the second hour of flight and I could feel the engine was running more freely - it just felt smoother. Oil consumption was very low, less than a quart in the first 10 hours. I cut open the filter after the first flight and was surprised at how little metal was in it. At 10 hours I changed the oil, cut open the filter and again was surprised by the small amount of metal in it. Now, at nearly 200 hours I'm getting 22-23 hours per quart of oil. I'm using Phillips XC oil and am adding Cam Guard in the recommended quantity. I didn't start using Cam Guard until the 50 hour mark.