Open the Library tab and your cassettes sit in a row, with the one you're looking at in front and its neighbors fanned out on either side. Drag or swipe and the shelf slides along.
Flicking
A gentle drag moves a card or two. A hard flick carries you a good way down the shelf, up to a limit, and it always lands on a card that's already been drawn. That sounds like a detail, but it means nothing pops in late while you're moving. The shelf just slides.
On the website's demo you can also use the left and right arrow keys. In the app, it's all touch.
What you see on each tape
Every cassette shows its label, and the colors tell you something about the files inside (see the tape types). The mini-player stays on top, so whatever is playing keeps playing while you browse.
When the shelf gets long
With a big collection, flicking is great for wandering and less great for finding one particular album. For that, jump to the Search tab. There's more on it in the search article.
Tip: if you like what you see, try the cassette view for the main screen. It shows whatever's playing as a full front-facing tape.