How do I determine which phone line goes where, without any special tools?
The simplest route would be to use a circuit tester on the various lines in your basement, and have a friend temporarily short the lines in each of the rooms.

An audible circuit tester makes this very easy. It can be a standalone circuit checker, or as part of a multimeter's functionality. It raises a voltage across a circuit, and if that circuit is complete current flows, sounding a buzzer.

If you have a multimeter, look for a speaker icon to see if yours can do this. 

As @lqlarry said, you could do this with a 9V battery but that shouldn't be needed - the voltage drop should be negligible.