Fuel management is definitely one of the hardest parts in the game to master.
Some pointers
-Fuel moves from the main depot to FSB via trains. Then from FSB to the PZGHQ via trucks. This is usually not a problem in the early game, but if any part of that process is disrupted, the end result is less or no fuel available for immediate use.
Note: While FSB is moving, no fuel will arrive to the PZGHQ of that sector (I.E. you won't get any more fuel to use apart from what you might have saved up from previous turns). The fuel is still stored up, but it won't get distributed until the FSB has finished moving. Basically this means there will be very little to no movement by panzer and motorised divisions while FSB is moving.
-PZG's in blitzkrieg posture(in which every German army is at the start), consume 2000 fuel at the beginning of every turn (to sustain the bonuses gained from said posture). That means 2000 fuel in AGN and AGS, and 4000 fuel in AGC. The amount consumed per PZG can be altered by a decision that happens in the early turns, but it can't be completely negated.
-Unsurprisingly, the biggest fuel consumption comes from panzer divisions, especially when they're in combat. Try to stick to rail-lines and plains when moving panzers, as movement in any other kind of terrain consumes much more fuel.
Now the most counter-intuitive tip: try to fight (and move) as little as possible with your panzer divisions. For maneuvers that necessitate lots of movement, try to use the motorised divisions as they're much more fuel efficient.
-Don't be afraid to leave some panzer divisions behind. They can be brought up later when you've excess fuel or with the "transport"-card. There isn't enough fuel to sustain all PZD's moving, not to even mention fighting, every turn. (If you wish, check out my "Second Wind" AAR
tm.asp?m=4338013. You can see a very fast initial German advance, as well as multiple panzer divisions basically immobile from turn 2 onwards, and then brought back into the fight later on.)
-Bottom line, there's never enough fuel. You just have to make do with what's available.