How do you prime a 2004 VW Jetta fuel filter?

Same way as any other TDI. Fill it full with 50/50 diesel and fuel additive then do short crank times till it starts. Then let it run at idle for 5 mins or so then take it for a short drive. Its the best way without using a vacuum machine

If it's a TDI-PD (Newer 2004 Engine, pop-off engine cover w/ no bolts) then hook up the return line and the supply line, but leave the line to the engine off. Cycle the ignition 7 times, waiting for the pump to stop each time. Then connect the last hose and it should start right up.
Note this won't work for the 2001-2004 (early) TDI engines as they do not have an in-tank fuel pump.