Memory does not get "used up"; you don't "finish using" it and then replace it. It is always re-used. In most modern computers that use Dual Channel mode in the RAM, the memory is installed as a pair of matched modules in a pair of motherboard sockets. Portions of BOTH modules are used at all times, not just one.
Unless you have deliberately defeated this feature (unlikely), Windows has a way to provide a huge memory reserve in addition to the actual RAM you have installed. If the space available in your RAM for current operations gets full and more is needed, Windows examines what is in use and decides certain portions are less used currently. It then copies all of that data onto a special file on your hard disk called the Swap File, along with notes about what this data belongs to. Then it marks that RAM area free and it becomes available for the next application needing space. Later, when the original application comes back in and wants to use the data that was moved out to the Swap File, Windows has to do that job again to free up RAM space, then copy back to RAM the old data temporarily stashed in the Swap File. Now, moving data to and from a disk file is VASTLY slower than using it in RAM, so this process slows down your application's speeds a lot. So a symptom that you have too little RAM, resulting in frequent use of the Swap File, is that programs you are using suddenly stop for a little while and the hard disk activity light turns on, then they start running quickly again. However, it is easy to confuse that situation with the normal operations of some programs that must use actual data files on the disk and are forced to wait for the disk to provide them.
When you have frequent Swap File use producing processing delays, "upgrading" your RAM can make a big improvement in performance. That is because there can be much more RAM space available for your application programs to use before it gets full, forcing Windows to use the Swap File. For example, Windows typically uses as much as a half GB of RAM for itself. So if you have 1GB or RAM installed, there's really only about 0.5 GB available for programs to use. But if you upgrade to 2 GB or RAM, now your programs will have about 1.5 GB to share - three times as much! If you often run several applications at once, that kind of upgrade can really improve performance.
If you upgrade, there are two likely ways. Remember, almost all modern systems will require that you install TWO memory modules, both of the same type and ratings (called a matched pair) in specific motherboard slots so that it can be used in Dual Channel mode. So you almost never replace one module. You may decide to replace BOTH of your existing modules with larger ones placed in the same slots. Or you might leave your existing ones in place and add a new pair in the pair of empty RAM slots on your motherboard. If there are no empty slots, this is not an option.
As a very rough guideline, if you already have 2 GB of RAM installed, upgrading to more then that is not likely to change your system's performance much. Few people other than advanced users run that much stuff simultaneously, but some do. Editing large photos and editing or creating video files may use a lot of RAM. If you have 1 GB of RAM and run a lot of applications simultaneously that seem to have slow-downs in them on occasion, upgrading your RAM may eliminate the slow-downs. If you have less than 1GB of RAM, the opportunity for improvement with more RAM is quite good.