My top tip for most computing, is don't be too afraid to experiment and play around with your computer, it's the best way to learn.
More linux specific? Learn to love the terminal.

You can do many things with it, including browse the internet with
lynx,
links2 or
elinks (+ others). Chat over msn, or facebook chat or many other formats with
bitlbee running through your favourite cli IRC client (mine being
irssi). You can use a variety of programs to listen to music, such as
moc or
cplay. You can download torrents through
rtorrent if you're into that sort of thing.
If you do go down that route though, how about a nice environment to run them all in, something that sits in the background and lets you resume your programs even after you've closed the terminal? Introducing
screen, it lets you run several items in a single terminal window, with keybindings to switch between them, as well as several other nifty tools. Others prefer
TWIN, not a program I'm familiar with (I'll confess now I'm a mere dabbler in all of the above, but have learnt to use most of them fairly efficiently even if I don't realise their full potential) but I've seen it mentioned as an alternative to screen.
If you take nothing from this, or you are interested, then check out this blog,
http://kmandla.wordpress.com linked a couple of times above, for inspiration on what can be done in the command line and on older hardware.
Don't forget to keep regular back-ups though.