Why is my bread so dense and moist?

I was watching a Lorraine Pascale (British baker / chef) episode on TV before. She had a saying which was "when it comes to dough, the wetter the better". Don't get tempted to add more flour if your dough feels wet. She also used a mixer with a dough hook AND allowed the machine to knead it for 5 minutes.

After kneading, gently shape the dough into a rough ball shape and with a floured finger press into the dough. If it's ready, the depression in the dough should spring back so you can't see where you pressed in.

I make bread a couple of times a week and usually have light fluffy results. On occasion though, I end up with dense and fairly wet loaf. This usually happens if I have been lax and not made it in a while and haven't bought new flour/yeast. It's important to keep (dried active/instant) yeast in particular in a sealed container and observe best before dates, else it will not work as well as it should. Make sure your bread mix is fresh and well before the best before on the packet.

It's difficult to describe the consistency of a well kneaded dough - there's really no substitute for finding someone to walk you through it so you can literally get a feel for the texture of dough that is ready. If you have any friends or family that bake their own bread to results that you are aiming for, especially if they use the same mix as you, ask them if they can show you how they do it and get your hands stuck in.

For a warm place in winter I usually set my bread for proving in a bowl by a radiator in my living room.

If the bread is not wet enough, the yeast don't activate. Follow the advice that Jonny gives above. If the bread still isn't rising properly, it is either too dry or the yeast might just be too old. Check the expiration date of your boxed bread mix, and follow the directions closely. Don't start experimenting UNTIL you have had success otherwise your own adjustments might be causing the problems you are having.