You ask for a systematic method. If there is only tab to follow, unless you know all the note names on guitar, it's difficult. When the music is there too, it's easier, provided you can name the dots.
Make a list of all the notes used, not including the accidentals with a #, b or natural before them. There should be 7, but not all notes are used in every song. See TTSTTTS to find the missing one or two.Put them in order, in a circle works best. Find the first note of the major scale they belong to. This is the one that gives a clockwise spacing of T T S T T T S between notes. T=2 frets, S= 1 fret. When you've found that note (A in the example above), you've found the major key.
When you've learnt the modes, you'll know that the 1st note is the start of Ionian, 2nd Dorian, 3rd Phrygian, 4th Lydian, 5th Mixolydian, 6th Aeolian, and 7th Locrian. Since the tune you mention is based around the B, the 2nd note, you can use Dorian.
You may notice that all the above 'belong' to A major, and all play the same set of notes, albeit with different tonal centres. E.g. E Mixolydian uses the same notes as A Ionian (major).
This may appear complex, but after doing it with lots of songs, it becomes easier. You'll probably find more songs in maj. (Ionian) or minor (Aeolian) than the others, depending of course on genre.