We just moved into a home that has a renovated basement and all of the receptacles have two CAT5 wires pulled to them (one for telephone and one for data) but none of the wires are labeled or terminated in RJ45 or RJ11 jacks. How do I test the wires to tell if they have data or phone signals?
If they are not terminated, they have no signals at all, until you terminate them and connect them to something.
Blue/white(with blue stripe) is normally the "line 1" pair in cat 5 cable used for phones. Green/white(with green stripe) is the standard line 2 pair, in the presently unusual case that you actually have 2 land-lines. Pins 4&5 for blue, 3&6 for green, on an 8-pin RJ-45. I would open the box (or the "Customer side" of the box if it's a Telco disconnect, not as likely inside the house - normally inside the house wiring is all yours) and look.
If you have a meter, it's easy (if tedious) to sort out the unconnected ones, if you are saying that you have a utility room that has a bunch that not terminated there either - strip a little and connect a 9V battery to a wire pair, then go looking for the other end with 9V across the wires you put it on. Label as you go, and it will get faster as you'll have fewer to check. Test leads with clips make this process easier but are not absolutely required.
Use reasonable care when testing for live phone lines - if it happens to ring, the voltage is significantly higher than the 48V you see when the phones are on the hook. On the other hand if it's completely dead (not as common with E911 laws) there may be no voltage at all.
Since they went to the trouble to wire a pair of CAT-5 cables at each receptacle, they likely wired them all back to a central patch panel in a closet or wall cabinet that looks something like this:
If that's the case, then none of the outlets are "live" and would need to be patched over to the appropriate service (data or phone). Unless they are patched to something, then they are not live. How to actually patch to phone or data varies depending on how the phone and internet service are wired to the wiring closet.
If they really just left the other ends dangling and unterminated, the best thing to do would be to terminate the to a patch panel like the one pictured (which is surprisingly easy with the right punch down tool)
If the jacks/wires are not labeled, you can trace (and test) them with a cable tester like this:
this is just one example of a cable tester - there are lots of cable testers out there of varying quality, but this is moderately priced and works well for home use. There are cheaper testers that just use an array of LED's to show you the cable status, and there are (much) more expensive testers that will do a full cable qualification to certify that it will run at the rated speed. I've used this model and it works well for home use, one nice feature it has for cable tracing multiple cables is that it has several numbered terminators that you can plug into one end, then when you plug the meter into the other end, it will tell you which one it sees