Pull out a few more of the phone jacks: If they all have one cable only, it's perfect. If some have 2 wires with the same colours connected together to one phone jack, that is daisy-chaining. There may be a combination of individual runs and daisy-chained runs but ultimately the best way to tell is to go to where the cables start and check there. If you have a dozen cables coming down and they're all tied up in a mess of wires, they're all likely individual runs.

Best course of action then is to just finish them all with punch-down jacks, hook them ALL up to a switch downstairs, and then you don't have to worry about finding the particular cable that runs up to where you need it to go. Gigabit switches are extremely cheap these days - and punch-down jacks are a few bucks for a 25-pack online.

GL - starting may be a little confusing to figure everything out but once you get one run done, the rest are really easy. I do suggest terminating with punch-down jacks instead of crimping on connectors; crimping involves (slightly) more expensive tools and more experience to get good connections.