There are many ways to speed up an aging or under powered system, you can begin by:
+ scan your computer for any adware/viruses/malicious software that can slow your computer down
+ running msconfig (windows key+r then type msconfig) and disabling all unwanted or non essential startup programs.
+ shut down all non essential or unwanted program from the system tray or using task manager (ctrl+alt_del then select task manager).
+ Defragmenting your hard disk can speed access to files and programs up.
if you a still not happy with the performance boost given by the above you can backup you personal data, format and reinstall windows then restore your personal data.
But ultimately the best way of speeding up your system is investing in more memory, a faster hard disk and better processor.