There's a lot to learn about playing Infinite Space, as evidenced by the fact that Sega has made a second tutorial video for the Platinum Games space RPG.
This video teaches one of the most important techniques in the game: skipping battle scenes. Every action in a ship battle is accompanied by a long sequence in which crew members call out what they're doing and prepare whatever kind of action is to be deployed. It's dramatic, and it lends the game a very "spaceship anime" feel -- but it also takes a long time. So, yeah, you can skip that after the first couple of times.
The tutorial also covers crew battles and, strangely, recalibrating your touch screen.