The supply map overlay tab in the lower right corner should show lines of supply, and you should be able to mouse over units or provinces along the supply routes to see more details.
If you've got a "Logistics Wizard" leader trait, they will reduce supply use for all units below them that are within range. A general assigned at Army Group level will use his Skill to reduce all units in range that are below him in the command chain. Keeping the units within their command radii can save a considerable amount of supply, which becomes far more critical at the end of a long supply line to a distant front.
I've played several Hungarian campaigns, and you really don't need to move anything away from your capital until you get involved in the war in 1940-41, unless you start one yourself. That means no supply penalties or costs for distance from your capital. You can even cheese the system by not providing any supply for a couple of years, then bring the army back into shape starting in late '39. I prefer not to game the system that far.
It's also a bit gamey, but you can reduce your "effective" IC briefly to less than 30 by changing your production law to something lower, to trigger the "Prepare for War" decision, then change it back to Partial Mobilization or as high as you can go after you activate the decision. That will gradually lower your Neutrality over the course of the next 10 months or so, to the point where you can DoW any of your neighbors, and spies can raise Threat on a target to make it possible even sooner. The lower Neutrality and increased Threat by a neighbor have the side benefit of reducing Consumer Demand, so you have more IC freed up to build military units.
In one campaign, I invaded and annexed YUG in Nov. of 1936 (drove directly toward the coast above Split, to literally "split" YUG, then took out the isolated pieces), took Romania in spring of '37 (easier with troops along the YUG border), followed by AUS and CZE before GER could activate Anschluss and Munich. After GER declared war on the USSR, I joined the Axis and managed to push my own invasion corridor all the way to two provinces short of Stalingrad. For supplying that, the two Transportation techs under the Theory tab were essential, and I had to research the Advanced Construction tech to improve an infrastructure "highway" to the distant front. Unfortunately, GER burned most of its manpower in a stupid invasion of Norway, leaving over 100 brigades (mostly armor and motorized) out of supply to starve in the mountainous interior. To complicate matters further, they then dumped at least 50 brigades onto my supply lines, taking everything I could send and leaving nothing for the troops at the front. I couldn't take on the Soviets by myself once GER collapsed, and the campaign ended in a crushing defeat.
Hungary is heavily dependent on the success or failure of its allies, since it has neither the Leadership nor the Manpower to match the major powers, even if it captures enough IC and resources. In a previous expansion of HOI3, I was able to build a couple of Transports and a license-built sub as a spotter, and pull off a successful sneak-attack invasion of England while they were distracted (GER then invaded at the last moment, taking 3 empty provinces), which gave me almost as much Leadership as Italy. The non-core penalties on Leadership are pretty severe. Hungary has the ability to punch above its weight if you play the techs right, but lacks the staying power of the majors.
Note if you're a recent newcomer: ORG is king in land warfare, so the land doctrines that increase ORG and Morale (ORG regain) are probably even more critical than the infantry equipment techs. You also want a high Officer Ratio, as anything over 100% gives you a combat bonus, up to a max of 140%, and units well under 100% break easily. Personally, I prefer to prioritize increase the starting divisions from binary (2xINF) to trinary (3xINF), and then add Artillery once they're all expanded. I also add an INF brigade to each of the 5 Corps HQs (HQ+INF), so they're able to chase away rival HQs (without inflicting a delay on your actual combat divisions), or to support an attack on a target from a third direction, inflicting an "outflanked" or "surrounded" penalty. Eventually, I expand them further into full combat divisions (HQ+2xINF+ART). If you haven't figured it out or read it, you can't "reorganize" a lone HQ and a lone brigade by group selecting them and then pressing the "Reorganize" button, but the "r" key will do it.
