You can measure/calculate a resistance using an analog input. Wire your circuit up like the push button tutoria: http://www.arduino.cc/en/Tutorial/Pushbutton
but replacing the pushbutton with the resistance you want to measure. This makes a voltage divider, with the voltage in between the two resistances equal to:
voltage = 5 * x / (R + x)
where R is the known (pull-up) resistor and x is the unknown resistance you're trying to measure. When you read this voltage with analogRead() you get a number between 0 and 1023, with 0 corresponding to 0 volts and 1023 corresponding to 5 volts, making the formula:
analog input = 1024 * x / (R + x)
Often, this value is all you need. If you really need to know the actual resistance, use this formula (assuming I did my math right):
x = AR / (1024 - A)
where A is the value you got from analogRead().