as soon as you get the notification that you can fast travel, open your map and select a destination connected to your current location.

figured it out somehow by myself, but it still seems not to work sometimes e.g. at home

I don't think you can fast travel from home, only from insurgent safehouses ?
Oh, and fast travelling inside a vehicule makes you leave said vehicule, so don't hope to get vics around that way

Fast travel is pretty buggy, i have good relations with Syndikat and it wont sometimes work, even there is no enemy around ...

Yea, it's super buggy.
I recommend the SSPCM cheat addon, it dosen't work for "old man" but it does enable the console.
From the console type in : player onMapSingleClick "if (_alt) then {player setPosATL _pos}". This will enable you to TP anywhere on the map by holding ALT and clicking. I use this when the fast travel doesn't work.

I got it to work, only once though, from home.