Axis & Allies can be frustrating at times. You'll often be forced to build your units far from where you need them, and loading all your land units onto transports to make an assault by sea is a slow process as well. Since you can't exactly sneak up on an opponent, you'll find they've stacked the territory you were planning to attack with defensive units in the meantime.
The key to success is to grind out a narrow margin of victory in every attack you make. This doesn't mean always winning a territory; it means making sure your opponent loses a greater value (in IPCs) of units than you do. And if you must sacrifice units, make sure you can hold the territory you attack so you recoup the IPC loss. Doing this successfully involves foresight and a bit of math. It gets easier once you get used to breaking down the odds of a given battle and adding up the IPCs spent on each side, and you can evaluate every attack this way.
Many players make the mistake of failing to build enough infantry. Infantry are excellent defensive units for their cost, but they're very useful on offense as well. For one thing, you need to have them around to soak up your casualties, otherwise you'll be losing your more expensive tanks and you'll quickly fall behind in the IPC race. In many cases, the attack strength of the infantry that can be purchased for the price of a more expensive unit is greater -- they're more efficient than fighters, for example.
Learn to use combined arms. Some units work well in concert as a natural result of their cost and comparative strengths and weaknesses (infantry and tanks are both needed for a successful invasion force). One of the better rule revisions added explicit combined arms benefits. Infantry are boosted by the presence of artillery, and tactical bombers work best with fighters or tanks helping them out.
Novice players will realize quickly that the odds are somewhat stacked against the Axis. Germany has difficulty controlling the Atlantic Ocean and faces the historic problems of a two-front war, battling the U.S. and Britain on one side and Russia on the other. Quick, decisive attacks in the early game can make a huge difference and lead to Axis success.
For their part, the Allies benefit greatly from cooperation and careful planning of maneuvers and attacks. Axis cooperation is limited by the vast distance between Germany and Japan -- they seldom are able to help each other directly. On the other hand, you'll often find U.S. units positioned in Britain, making attacks on Axis-held territories on the continent. If the Allies can gain a toehold in Western Europe, they can close in on Germany like a vice.
You certainly don't need to be a genius strategist to enjoy Axis & Allies, but it's fun to pull off a thrilling victory every once in a while.