How to make a cake less dense

What you are making is a pound cake. Or maybe a sponge cake, depends on the order of mixing the ingredients. Of the two, the sponge cake is somewhat lighter, so if you have been making pound cake (cream butter and sugar, add eggs, then flour), you can switch to sponge (foam eggs and sugar, add flour and fat). But both are hearty homemade cakes, they are supposed to be dense.

The iced cakes you get in a bakery are much lighter, because they use a different type of layer. Most types of cake are lighter than pound and sponge cakes. Try making genoise, chiffon, or angel food cake layers, they are all light. And yes, using cake flour will help too, or replacing part of the flour in the recipe with pure starch (usually cornstarch or potato starch, you can also use wheat starch if you can get it. Tapioca or arrowroot aren't that well suited). For a real "pro" taste, also throw in some lecithine, it makes the mouthfeel softer and smoother - but if you don't feel like hunting around for lecithine, don't bother, a good homemade cake doesn't really need it, I only mentioned it because you asked about "cake made by a pro".

You are essentially correct. It is important to beat plenty of air into the butter/sugar/egg mixture initially, but you should mix in the flour until just incorporated to avoid over-developing the gluten, which will result in a dense cake.

You can also try using cake flour, a low-protein white flour that helps the cake stay light.

The self-raising flour could be part of the problem. Chemical leavening can lose its power over time, especially if exposed to humidity. Consider using cake flour (which may make for a softer crumb, too) and adding your own baking powder. This lets you ensure that the leavening is fresh, and also lets you control the amount.

Also, if you really want light and airy, mix up an angel food cake. It's pretty much the ultimate in light and airy as cakes go, and very easy to make.

Try this:

200g of self raising flour  
200g caster sugar 
a tsp of baking powder 
tbs of water and 
four eggs 

Whisk the eggs in a bowl. In another bowl mix all other ingredients together, then add the eggs add a bit of vanilla essence.
Whisk for 2 mins, then bake on the shelf second from bottom for 45mins at 150°C.

You will have a light, fluffy, moist cake. All you may need to do is trim off any crusty edges.

Duncan Hinez or Betty Crocker cake mix makes light cakes.