On the 737 you'll get a FMC/CDU message alert; "Using reserve fuel", whenever the box figures you'll be dipping into the manually entered reserve fuel. (It basically compares anticipated fuelburn with the rest of your active route.) This Reserve fuel is alternate fuel+final reserve fuel.
Now, your final reserve is fuel for 30 min holding at 1500' at holding speed. 1100 kg's is what we use.
In Europe, the only approved phrases to get priority is either PAN-PAN or MAYDAY. A low fuel call, will not give you priority.
If I'm down to reserve fuel (typically 2,3t), I either divert or commit to my destination (informing ATC about it).
I call PAN-PAN if I anticipate to dip into my final reserve(1,1t), and MAYDAY if I'm in fact burning it.