The resistor can go on either side of the LED, doesn't generally matter.
An LED won't take exactly 1.8v, or 1.984v, or 2.2244821v... it will vary with current, however, it won't vary much. Assume that the voltage is on the low end of 1.8v. Determine the current the LED expects (most LEDs are specced for 20mA though its common to drive them at 10mA to increase life) or that you want to drive it at, then choose a resistor based on (Vsupply - Vled)/I = R. Then, measure the voltage across the LED and you have that LEDs typical voltage. It'll vary slightly if you change the resistor or the current....
If you double the voltage on a resistor, you double the current through the resistor. If you double the voltage on an LED thats already on, you'll get massive current (for a short time).
It is also common to use a current source instead of a voltage source to drive LEDs, then you don't need to worry about the voltage as much.