This is a fastener-by-fastener description of how I diagnosed and repaired a slow coolant leak as a result of a bad coolant hose flange on a 2001 VW MKIV Jetta Sedan with automatic trans and 2.0L (AEG) engine. This is a known issue with VW engines including the MKIV, and it is the most common cause of a slow coolant leak for this vintage engine.
Note that the coolant used in many VW engines is G12, only available through the dealer. Literature published by VW explains that G12 is not compatible with other coolants, including universal coolant sold elsewhere. They warn that mixing G12 with other coolants might cause engine or seal or sensor damage, and that their warranty may be void if there is evidence of coolant mixing and damage resulting from that.
There is another useful description of how this repair is done at the following link done by MikeWire on the VW Vortex forum.
This video is posted for entertainment purposes, and is not an instructional guide. Do not attempt this at home without professional advice. I am not a professional mechanic, and any misadventure resulting from your attempt to repair your vehicle is your responsibility.