There are two principle methods depending on the airline;
Automated: 'A computer' either onboard or somewhere in the ether connected via ACARS will generate a FLEX temp based on the prevailing conditions and limitations (e.g. from the ATIS, AIS etc). This method is very opaque to pilots as 'what happens under the covers' is completely unknown. It's a good idea to do a 'does that sound right for these conditions' sanity check on this data.
Manual: Using paper based performance manuals specific to an airport, runway and even intersection. This gives the pilot a maximum and actual figures but because it involves alot of this number divided by that number multiplied by the first number you thought of... has HUGE potential to contain errors and therefore should be cross-checked by both pilots. Boeing manuals are much easier in my limited and humble experience for manual performance calculations.
DM...