Along the rows or across the rows
On a two-row melodeon most notes can be found in more than one place. Playing along the rows means keeping to the row in the tune's key. Playing across the rows means using both rows to save changes of bellows. Plenty of players mix the two.
Along the rows
Each row of a melodeon is a scale on its own. The G row of a D/G gives the notes of G major, the D row the notes of D major, one on the push and the next on the pull. So a tune in G can be played entirely on the G row, and the bellows change direction almost every note:
That's six changes of bellows in eight notes. Each change puts a tiny gap and a fresh attack into the sound, which is what gives along-the-rows playing its bounce. It suits dance tunes with a strong lift, and the pattern is so regular that it's quick to learn.
Across the rows
Every note in that scale except C is also somewhere on the D row, and some are there in the opposite direction. Mix the rows and you can play long runs without turning the bellows round:
The same eight notes now take two changes of bellows, at the cost of four jumps between the rows. The notes join up more smoothly, which suits slower tunes, airs and anything you want to sound legato. On a B/C or C♯/D box you cross the rows all the time, because in most keys neither row holds the scale by itself.
Look at the first note. G is on the push of 3′ and on the pull of 4. Across the rows, the pull wins because the next few notes are pulls too.
What decides it
Playing across the rows isn't better, and along isn't for beginners. The question for each phrase is what you want it to sound like, and what your left hand needs: the bass buttons give different chords on the push and the pull, so the bellows direction has to suit the chord as well as the tune. The bass side explains why.
Within a single tune you'll often play one phrase along the row for its punch and the next across for its line. The scale pages show both ways for every common key, so you can see which notes give you the choice.