How important is the creaming process while making a cake? A few of the chocolate cake recipes I read always start with the step - mix butter and sugar until creamy. I've tried a couple of times but failed to create anything near to creamy. But a few recipes completely eliminate the creaming process, wherein the wet ingredients are added directly to the dry mix. I'm looking for a cake which has a light and moist texture. What should I do? All my previous cakes were either too airy or grainy! On a side note, no matter how much time I mix, I'm not getting the sugar to completely dissolve in the butter. Should I be adding more butter?
The purpose mixing the butter and sugar until creamy is to distribute air through the batter that will help leaven the cake in the oven. Skipping this step can create a denser cake.   You want to add the air into the batter before adding the flour in order to prevent over mixing, which creates gluten; causing a tougher texture. 

Beating the eggs until foamy and folding them into the batter or adding the eggs to the butter/sugar and beating until fluffy will also create a lighter texture. 

The sugar does not need to dissolve in the butter, but it should be evenly distributed. This site gives a good visual on how creamed butter &amp; sugar should look.