As a beginner I got axis and allies 1941 and noticed the game has only 4 dice and very few pieces. I had to use a lot of substitution chips (they can get confusing) and make my own paper slips with the units name on them. Where can I buy additional units and dice?
There are various places you can shop online for spare pieces. One such location is at http://www.historicalboardgaming.com/Axis-Allies-1941-2012_c_196.html
Alternatively, simply getting an additional copy of the game from a yard sale might be more cost effective at times.
As for dice, to my knowledge they are standard d6 with a special symbol in place of the 1, but functionally they are the same otherwise. I have been very pleased with the quality of dice from http://www.chessex.com/ and I regularly visit their booth at conventions.