Walking around the track and...
Walking around the track and seeing each corner from as many perspectives as possible will speed up the learning process. Television and video games do not show many elevation changes; seeing the track in person will reveal many aspects you won't find otherwise-even while riding.
If you are lucky enough to be attending a world-class track that is featured on a video game, this provides an excellent source for learning the circuit. Today's video games are astoundingly accurate when it comes to the track layout, and playing the game will not only force you to learn the course but also select some lines to start. Unfortunately, this is not an option for most tracks in the U.S., but it is definitely worth exploring if available.
Now that you are familiar with the track from a birds-eye view and a rider's perspective, you can fill in the gaps by watching a race from an event at the track on television-again, if it's available. Why not do this first? Typical race coverage jumps from turn to turn so quickly that in most cases you can't identify the actual turn until it's too late; the scene has already changed again. You will be surprised at how quickly-once you've watched some onboard video-you can identify each corner as it appears and then make use of what you see. This is your opportunity to find not only more line choices and reference points, but also aspects such as passing zones and other nuances you won't find elsewhere.
If you have a chance to go to the track and watch motorcycles go around, even better. At most tracks, there are plenty of spots to watch and if you can see each corner in person that will give you even more insight into each turn's character. If you have the chance, walk around the track as well for an even better perspective-err, preferably not while the bikes are going around. A track walk will give you plenty of time and opportunity to find more reference points as well as camber and elevation changes that you may not notice otherwise. If you've ever stood at the base of the Corkscrew at Mazda Raceway Laguna Seca, you'll know that video games and television can't express the magnitude of the drop off at the top.
When it comes time to actually ride a new track, there are a couple of things to keep in mind. First, our brains tend to think in repetitive, geometric shapes such as 90-degree angles and even surfaces. But racetrack designers purposely avoid exactly those characteristics in order to make a layout more challenging. There are many examples at tracks around the world where two corners are similar, but not quite identical. Our natural inclination is to try and make the turns identical, whereas the correct approach is to treat the two turns as distinctly different. Second, as your inventory of tracks you've attended grows, you'll find that you can speed up the learning process by considering a certain turn at a new track similar to a turn at a track you know. While this is definitely helpful to a certain extent, try to avoid a similar situation of considering the turns identical and navigating them the same. No two turns are identical, whether it's camber, available traction, radius or some other characteristic that differs.
As you take your first laps of the new track, find the reference points that you've picked out beforehand, noting differences or similarities to what you expected based on your research. It may be helpful to take the first couple of laps a bit slower than you would otherwise, just so that you can take in the scenery. Some of these reference points may end up being discarded, while others will be useful; catalog each accordingly, while keeping on the lookout for new reference points; you may be surprised at what you'll find unexpectedly. Once you've spun a few laps, refer back to the other material you've collected; the satellite view and onboard video especially will reveal even more once you've actually ridden the course.
Riding a track for the first time is always a fun experience, as it presents new challenges and adds variety; many riders find the adventure can kickstart their skills after having become complacent with riding the same track all the time. Going prepared to somewhere new and having familiarity with the track can benefit racers and trackday riders alike by boosting confidence and easing the trepidation associated with the unknown.