I would check two things first, as they are they most common reasons for dense cakes.
First, how do you measure your flour? Many beginning bakers start with the 'dip and scoop' method. Dipping the measuring cup into the flour container and scooping it out packs in too much flour. This will cause a dense cake. The most correct way to measure flour is by weight. However, if you don't have a kitchen scale, you'll get much better results by stirring the flour in the container to lighten it, then spooning the loose flour into a measuring cup. Level it off with a straight knife.
A second thing that commonly causes a dense or tough cake is over beating. Overworking the batter develops gluten, like bread cough. As a rule, stir in the flour until just combined and smooth. You beat the air in during the earlier stages of creaming the butter & sugar, and beating the eggs. Once you start adding the flour & liquid, you want to keep the beating to the minimum required to make a smooth batter.
As far as dryness, the most common cause is overbaking. You really can't go by just the timer. Start checking early. While most recipes tell you to use the toothpick test, there are several other sensory clues to doneness. I find that by the time a toothpick comes out 'clean', the cake is overdone.
The first thing you'll notice is smell. A soon as you begin to smell the cake permeate the room, start checking. The first visual clue I find is when it just starts to pull away from the side of the pan. Don't wait until it's pulled loose on all sides, just the beginning of it pulling loose usually means it's ready. Lightly touch the top with your finger. If it gives slightly but springs back immediately, it's done. If it doesn't give, it's too late!
The toothpick test is only a last resort. People have different interpretations of what 'comes out clean' means. It really means that any crumbs attached to the pick are cake-like and not batter-like. You can easily brush them off without getting gooey. If you wait for the toothpick to be totally clean, it's too late.