Your basement has the potential to be the ideal gym. The first thing you need to do, if necessary, is remove the television, computer, and/or telephone. When you're working out, you can't have any distractions. You need to be supremely focused. Of course, a radio is okay. Make sure you get some albums or download songs that motivate you. It would be wise to have a large collection. You will be down there for one to two hours three to five days per week. That time adds up. You don't want to be listening to the same songs over and over again. That can have a negative impact on your motivation.
The next thing you need to do is set-up a carpet in a spacious area. If you have a bench, which would be beneficial, place the bench in the center of the carpet. The carpet is important because it allows you to toss dumbbells on the floor after you struggle for your last rep - or if you get into trouble. Also a squat rack and a chin-up bar are great additions to complete your home basement gym.
Keep in mind, when doing chest presses without a spotter, use dumbbells, not a heavily weighted barbell. A barbell is too dangerous and could cost you your life. If a weighted barbell falls onto your neck and no one is around, you're going to be in serious trouble. It's happened too many times before. Don't be a hero. Play it safe. Dumbbells are more effective anyway. They recruit more of the smaller muscles necessary to complete the exercise.
If you don't have a bench and plan on using dumbbells for presses, you can lay on the floor. This is a better approach anyway because you're not getting any help or leverage from the rest of your body. The only reason you don't see this in the gym is because it would look strange to see a bunch of people lying on the floor doing presses.
Since it will be difficult to go up in weight in many situations considering you most likely won'’t have a spotter, it's important to implement supersets. They will tire your muscles and make less weight feel like more weight, which will in turn increase muscle strength. You should also do this to a lesser extent with drop-sets. They will also help strength, but mostly muscle endurance.
Take these steps to build a great gym and body!