Minor with a raised 6 — natural minor's b6 lifted a half step, and the gloom gets a window. That one note flips the 4 chord from minor to major, so the classic tell is a minor tonic vamping against a MAJOR 4: 1-⁷ to 4⁷, round and round. It's the cool minor — funk, Santana, modal jazz — sad enough to mean it, bright enough to dance to. If a minor song's 4 chord is major, you've left natural minor; you're here.
The natural 6 — a raised 6th in a minor room; the window that keeps the gloom from settling.
Your tonic is the 2 of the parent — the major key one whole step down shares every note. D Dorian is C major's set with D as home.
The raised 6 clashes with anything built on b6 — if the changes bring a b6 major or a 4-, the harmony has voted natural minor and Dorian's window slams shut. Listen for which sixth the chords are using before you commit.
'Scarborough Fair' (songbook again) is pure Dorian; Santana's 'Oye Como Va' is the 1-⁷ → 4⁷ vamp verbatim; Miles Davis's 'So What' rides it for the A sections and lifts the whole thing a half step for the bridge.