Backup your files, wipe the drive clean and then re-install the OS. Sometimes over the years you accumulate files you don't need which slow the machine down. This could include built up temp files which never cleared out (which could include the system and applications cache files), some of which can cause errors. Your disk permissions could also be not what they should be, or maybe your disks are fragmented. There's lots that could cause your system to drag on that may not even be hardware related. I'd recommend checking software problems first before you start spending on hardware since it might not be necessary. A clean install of the OS will fix many of the aforementioned issues as well as many others that may not have been considered. You can also try to create a new user account before doing the wipe and play around with it. Sometimes only certain user accounts are associated with the computer slowdown. If that's the case it would just mean a matter of creating a new user account and migrating your files over to it.
Also consider how old your computer is. Sometimes if its many years old, its not worth upgrading and it becomes more cost effective to buy a new machine. Check to make sure that your system profile meets the specifications of your specific OS and applications that you use.
If you are looking for an upgrade of hardware, an SSD will cost you an arm and a leg, but they cause your system to fly if your system bottleneck is your HDD.
Hope that helps.