How to Win at Everything Forever[edit]
Panzer General simulates combined arms, and for the most part it captures the realities of World War II fairly well - tanks are terrifying on open ground, infantry are imposing in cities, woods, and fortifications, and artillery is the queen of the battlefield. The problem is that in Panzer, bombers are the undisputed king, by which I mean they kill everything. A 5-star, 15 strength Ju-87D Stuka can often kill a unit in one turn, including Air Defense units with low initiative (all except the 8.8cm/3in/90mm heavy air defense units). A 5-star B-29 Superfortress laughs at the enemy's puny units, which can't even hurt it - even fighters will get reamed unless they're 3+ experiece or jets. Needless to say, this isn't historic - not even modern bombers with laser-guided munitions can win without ground forces.
But since fighters can still shoot down those glorious bombers, or at least limit your targets, you also need your own fighter force. Starting from a 1939 or 1941 start, the strategy is to get a couple extra tanks and artillery pieces so you can have 2-3 task forces each with at least 3 infantry, 2 tanks, and 1-2 artillery pieces. Then just buy fighters and bombers for core, always having at least two more fighters than your total bombers. As for bombers, have at least 3 Ju-87Ds, then branch out to get a few Ju-88As or He-177s. Level bombers leave a unit suppressed, so if you bomb a high-defense tank or entrenched city infantry with two level bombers they'll probably only hit back with half strength.
The one extra fighter flies over your route of advance first, sparing your bombers if you happen upon enemy air defense and scouting for you. Try to fly into clear terrain, since most air defense units hide in woods, cities, or hills.
To conduct an attack, bomb enemy tanks, then kill them with your tanks while advancing the infantry and artillery into place to shell any dug-in units next turn. Attack artillery or slow air defense units with tanks from behind, and then wipe out cities, forests, fortifications, and mountains with infantry, leading with Pioneers or Engineers, which can't be hit by rugged defense.
If you're playing a campaign, this even works on most defensive missions - Byelorussia (aka Belarus) can literally be won on the first turn if you just place your best units front and center and just bull rush their one key city.
How to Defend Yourself, the Nice Way[edit]
This is by-the-book military strategy: a mobile defense plus strongpoints along defensive terrain. The idea is to find some good natural cover, like behind a river or inside a line of woods, and plop down infantry to dig in with air defense and artillery behind them. You usually start with a decent line if you're defending.
The key is knowing when to pull back and when to push forward. Eventually part of the front will break, and you need to make a quick decision to either send in your tanks and planes to throw back the enemy assault (recommended if you have a river and decent resources, like in Stalingrad playing as the Russians), or to pull back your forces to the next line of defense.
How to Defend Yourself, the Cheap-Ass Way[edit]
This is another game-breaking strategy, and will win most of the harder defensive scenarios early in the game. Usually there is an armored unit that's very cheap - the PzIA and PzJgIB for the Germans, the TKS for the Polish, the Matilda I for the British, and to a lesser degree the BA-64 for the Russians. If not, you may also have cheap ATGs (preferable) or infantry. BUY A HORDE OF THEM AND DON'T STOP. As defender, you get a small fixed amount of prestige each turn based on the number of key cities you have left, and if you can buy crap units faster than the enemy can kill them you win by default
How to Defend Yourself, the Sadface Way[edit]
Unless you're playing a campaign and have a sizable fighter force, it's impossible to win Cobra. Don't even try :(