The basic process is fairly straightforward - your script just searches for the BBCode tag and replaces it with the HTML equivelent.

For example, for bold it would search for [b] and replace it with <strong>.

It can get complex when you start dealing with complex BBCode (for example, Invision Board's BBCode parser comes in at just under 4,000 lines of code) but don't worry about that for now

Also, there is a BBCode extension which may help - PHP: BBCode - Manual

Alan