Dm7b5 (D half-diminished seventh) is a four-note chord made from D, F, Ab and C. A half-diminished chord is a diminished triad with a minor seventh on top. It is the ii chord of a minor key, so it opens the minor ii-V-i that jazz leans on.
Built from the root D, the minor third F, the flat fifth Ab and the minor seventh C.
Frets from low E to high E; x means don't play that string.
Easiest shape to start with: Open position (xx0111). It has 1 open string, nothing above fret 1 and 2 muted strings.
Every note of Dm7b5 is in these keys. The numeral is its place in the key.