This is a fairly common PC question. Now there are numerous tips and tricks you can do on the software side. Some work and some don't. As far as hardware goes, one of the quickest ways to add speed is to add more memory (aka: RAM or Random Access Memory). You'll probably see more difference with a memory upgrade than most other's aside from perhaps a new video card. How do you know what to add? Well with the numerous different hardware configurations it can be confusing. Some memory vendors or manufacturers websites can help you a lot. I'm going to highlight a couple of my favorites.
First up is Crucial Technologies. Crucial I've used many times and I've been very happy with both service and they are reasonably priced. If you go to the Crucial home page you can look up what you need both manually and automatically. To use manual method(Aka: Crucial Memory Advisor Tool)you need to know the manufacturer of your PC and model number. If your unsure or if you have a custom or home built PC you can use the "Crucial System Scanner". This will scan your PC and tell you what you can use. They'll give info on your PC such as how much you memory you have, how many slots you have open and what your system can handle. FYI if you use Firefox or Opera as a browser you have to download a quick add-on. Otherwise just switch to Internet Explorer. The memory is guaranteed to be compatible with your system.
Another vendor that has a similar set up is MemoryStore.com. Same idea though . You can look up your memory either by manual method or a system scan. I like the system scan method because it takes out much of the guess work. Other manufacturers to try out are PNY and Kingston Technologies are alternatives to try (without the system scan). I wish you luck and happy computing!