To begin, preheat your oven to 350 F and make sure to grease and flour three 8-inch-round baking pans. If you don't have three pans, you can bake each layer separately, one at a time.
Next, in a large bowl, combine the butter and sugar until the mixture becomes light and fluffy. You can do this by hand or use a standing mixer with the paddle attachment.
Add the eggs one at a time to the creamed mixture, making sure to beat well after each addition.
In another large bowl, mix together the cake flour, baking powder, and salt.
Alternate adding the flour mixture to the butter mixture with the milk and vanilla extract, making sure to mix well after each addition until you have a smooth batter. It's important not to overbeat.
Once the batter is smooth, divide it evenly into the three prepared pans. Bake for 20 to 25 minutes or until a tester inserted into the cake comes out clean.
After baking, let the cakes cool in their pans for 10 minutes. Then remove the layers from the pans and allow them to cool completely on wire racks for 1 to 2 hours. The cakes need to be completely cold before you can start frosting them.