The first thing I would do is make sure you have antivirus/firewall from a reliable vendor like mcafee.. make sure it is enabled, configured, and properly automatically updating.. try a forced update and perform a complete scan of the computer.
You might also want to get a good antispyware program like spybot S&D from http://www.safer-networking.org
to ensure you aren't bogged down by that stuff.
I wouldn't install anything else tho.
You'll want to check the CPU speed and the amount of RAM the computer has. Right-Click on the My Computer icon >> properties >> on the general tab that comes up first it should tell you CPU speed in ghz and RAM in mb or gb
If the CPU is very slow you'll probably just want to get a new computer.
If the RAM is just low, you can usually upgrade it.
If browsing the internet is slow then that would mainly be from your ISP.. their speed and possibly the ISP speed of the websites you're going to.
You can try clearing the browser cache and defragmenting the harddrive but these do not do much... they may just make things go a tad teensy tiny bit smoother.
You might want to check how many programs and services are running in the background. Turn off any flashy splashy windows themes.
Definitely check the amount of free harddrive space left on the harddrive. If yu are running out of space this can make windows run slow and then begin to crash until it basically won't be able to run at all. You can upgrade a harddrive.
Good Luck.