Does the noise go away when you turn down the volume control? If no, you may have the jack wired backwards or missed the ground from the jack to the pot. If yes, it's the pickup or something else upstream of the volume pot - maybe a missing ground connection. Does it have a typical Tele-style metal control plate? If yes, check that the pot nuts are really tight. If no, you need to 'manually' ground the casings, which is not shown on typical Tele schematics because they assume there is the metal plate.
If the noise does go away when you turn the volume down and the pickup appears to work (as in producing a signal) does it go away (or reduce substantially) when you touch the strings? If not, you need to ground the bridge. With old Teles this happens automatically via the shielding plate on the bottom of the bridge pickup, but with any other type of pickup (and most modern Tele-style ones) you need to add a wire to do it as well.
If it all appears to work right, the noise goes away when you turn down the volume and is reduced when you touch the strings, does it go away when you turn round holding the guitar - can you find a quiet orientation? If so, I have bad news for you... that's typical single-coil pickup noise and there's nothing much you can do about it. You can do all the shielding and star-grounding possible and you still won't eliminate this, it's magnetic noise and the only cure is hum-bucking pickups of some sort.
Sorry, a lot of questions! But it should be possible to identify the fault, at least.
