One metric for how similar languages are to each other is based on the concept of Linguistic Distance. Unlike some approximations that are more subjective (ie. This languages sounds a lot like that language), linguistic distance is quantifiable. This is important because it gives a concrete comparison of two languages.
Using a statistical approach (called ...
All credit to Mitch for this answer, but a very similar question was posted to Linguistics.SE:
There are qualitative and quantitative measures for 'distance'.
Qualitatively, many languages are easier to compare simply by know
something about their family tree, which is implicitly recognizable
(if one is lucky enough to know so many languages so ...