LinnStrument's pitches are arranged like the notes on any stringed instrument: each row consists of consecutive semitones, and the rows are offset from each other by 5 semitones, as on a bass guitar or the lower four strings of a guitar. However, you can tune the rows however you like by using the Row Offset settings in Global Settings.
The following diagram shows the note names for all 200 note pads, as well as the fingerings of common chords and scales in the default Fourths tuning. Click it for a larger view:
The chords and scales are shown in the key of C, except for the A Minor scale. To transpose any of these chords or scales to another key, simply move your hand left, right, up or down, keeping the same relative finger position, or shape. That's the beauty of LinnStrument's isomorphic note layout: you only need to learn one chord shape for all 12 keys. Compare this to a piano keyboard, which requires that each chord has a different shape for each of the 12 keys.
Here's a video that demonstrates where the pitches are and how to play basic chords, inversions and scales:
Here's a drawing showing the location of the natural notes on the musical staff, submitted by LinnStrument owner James Weaver (Twitter: @JavaFXpert):
Here are some good resources for learning to play LinnStrument: