The sheen on a new tire is the release agent applied to prevent the tire sticking to the mold that formed it. That thin layer of release agent is as slippery as hell until it's scrubbed off, and you'll only do this by riding.
So imagine your tire's contact patch is the palm of your hand. The center of the tire will quickly scrub, but that's the easy part. Just don't accelerate too hard straight off or you'll get wheel spin. The best approach to scrubbing the edges is not to ask too much too quickly.
Gradually leaning the bike over a little more at a time will steadily remove that slippery sheen. Looking at your palm, imagine as you lean over that you're introducing un-scrubbed are to about a quarter of your palm at a time. The majority of the contact patch needs to keep offering perfect, scrubbed grip.
What you don't want is for that palm-sized contact patch to be 100 percent un-scrubbed. While your tire fitter will recommend a fail-safe amount of kilometers, it's probably more than you need. Whether on the road or track, taking the same amount of time to scrub tires in as it takes you to warm them up is a safe bet.
You can control the process better on the track as you do your two or three warm-up laps, just lean a little more with each corner, and be aware of how much you have leant up to that point.