Dorian and Mixolydian
Of the five "extra" modes, these are the two a first-position player actually meets — all over folk, fiddle tunes, and rock. Each is one note away from a scale you already know.
Dorian — minor with a raised 6th
Dorian is the natural minor scale with its 6th degree lifted a half step. That one bright note stops it sounding fully mournful — it's a hopeful minor.
Compare it to plain E natural minor — only the 6th changes:
Mixolydian — major with a flat 7th
Mixolydian is the major scale with its 7th degree lowered a half step. No leading tone straining up to the tonic — so it sounds like major with the edges knocked off: folky, grounded, a bit ancient. Bagpipe tunes, sea shanties, and a huge amount of rock live here.
Try it
Try
Play When the Saints Go Marching In in G major. Now play it again, flattening every F to F natural (low 2 on the D string). It shifts from a bright march to something older and folkier — that's the ♭7. Then play a G major scale and an E natural minor scale, and put a ♯6 into the minor one (C♮ → C♯): now it's Dorian, minor-but-lifted.
The usual mistake
Playing the characteristic note "in tune" the way your hand expects. In Dorian, the 6th wants to be high (against your minor-key habit of a low 6th). In Mixolydian, the 7th wants to be low (against your major-key habit of a high leading tone). Your fingers will fight it — override them, and listen for the mode.