If you have purchased an older house, you may not have as much insulation in it as you would want to have. That means that your house isn't going to stay at the same temperature as easily as you would like it to. It also means that you are going to pay more in heating and cooling costs than you might like to. One thing that you can do is to talk to a company that installs insulation and ask them to come out to evaluate your house. They will be able to tell you what your options are and will suggest various kinds of insulation to you. You have several kinds to choose from.
This kind of insulation usually comes in long rolls that are cut to the width of the space in between two studs or joists. The rolls can be cut into sheets that can be packed into that empty space and fill it up from the floor to ceiling, or from wall to wall, depending on whether it is going into a wall or into a floor or ceiling. Batt insulation is generally pink, and it is usually made out of fiberglass. It is what most people tend to think of when they think of insulation. The R-value any batt has depends on how it is made. In order to install this insulation, space has to be made, and that will mean taking down walls, so if you are doing reno work, this can be a good choice, but it is harder to retrofit without structural changes.
Another kind of insulation that you might want to think about is blown insulation. This is usually cellulose, but it can also be made of cotton fibers or a mix thereof. The cotton fibers are generally some kind of recycled clothing or material that is shredded and turned into insulation. The insulation comes in compressed packages, then is put into a machine that fluffs it up. A hose is then connected to the machine, and the nozzle of the hose is put into a hole in the wall and the insulation is blown in. Blown insulation can be a good choice for a retrofit because the existing walls will help to keep the insulation in place. The techs from the insulation company will have to cut holes in your walls, but they will be relatively small and easily patched.
If you have purchased an older house, you want to make sure that it is as weather-tight as possible. One way to do that is to add on more insulation. Consult an insulation company to see what they recommend for you.