My first game I played as the allies and rage quit after not doing very well.
My current game I've only played as the UK (includes Canada) and Americans (letting the AI control the other allies and Russians) and I've learned a heck of a lot by finally managing to kick the Italians and Germans out of Africa and make a landing in France late in '42 and Italy in early '43. Learn the difference between transport and amphibious transport! I did not at first and it hurt my landings.
I've been a little gamey as I took the British Expeditionary Force and marched them through France and then transported them to Africa. I then did all I could to ship almost a dozen units (thank god the AI didn't go for Sea Lion) to Africa.
As the allies I think you should take advantage of the fact that the Italian navy usually doesn't come out to play until late '40 early '41 and get those units transported and in place to repel the Afrika Corps. Make sure to 'operate' at least one or two bombers and fighters as well as ground units. Also, I invested in an Engineer units and sent them to Africa to build some fortifications. I let the Germans and Italians attack me and then went on the counter. I probably should have counter attacked harder since I think with a more aggressive approach I could have kicked them off the continent at least 4 months earlier than I did.
It's been interesting to watch the Germans and Russians duke it out. The Germans have managed to take Stalingrad and Leningrad but not Moscow and now they have had to divert some of their forces to cover against my landing in France. Sometimes I have felt that the Russians should keep their units entrenched rather than attack a German unit, especially when the Russians have a good defensive line set. I felt that is one of the the things that contributed to the fall of Leningrad.
Also, they did a great job of building fortifications outside of Moscow but didn't do anything outside of Leningrad and I felt that they over protected Moscow when they could have spared a few more units to protect Stalingrad which at it's peak only had four units defending it. The Italians are holding Stalingrad so I am confident the AI will take it back if they simply devote more resources (units) to the effort. I'm almost tempted to take control in the East.
I want to note that I am playing on normal with no bonuses to anyone. The Americans are finally starting to get some serious MPP and I don't think the Germans have enough subs to try and attack my American transports. I hate to lose units which I think is going to hamper me in France since I think I should just be trying to slug it out with the Germans and if I lose some units that's okay since I can replace them fairly easy. While if I can hurt or destroy some German units they will find it much harder to replenish or replace them.
I've definitely learned to keep my ships in big "stacks of doom" in the Atlantic near Germany and the Med. I only split up my destroyers to protect my shipping which those damn U-boats keep hitting. In my first game I separated my Atlantic fleet into three groups and the Germans used some really good hit and run tactics and then took my down in two separate big battles which hurt them but decimated my Atlantic fleet.
With your Carriers, make sure you pay attention to the mode you have them in! For a long time I had them just as fighters rather than tactical/Naval bombers.
Don't ignore diplomacy. I did in my first game and then invested too late and finally quit when Nationalist Spain joined the Axis.
And really don't ignore research. Make sure you can fight on the ground and get all those production techs and logistics up a few levels. When you start getting those huge MPP's each turn you will be thankful for the early sacrifice.
I'm really enjoying this game even though sometimes I get frustrated. Sometimes it's because of some unlucky dice roles but mostly it's because I made a dumb mistake and the AI rightfully punishes me for it.
I think when I become a better player at this game I am going to play a game as just the Russians and see how I do against the Germans without having to worry about any other fronts.