If the only information you have is what the user searched for, then the
simplest thing to do is recommend topics based on the topics that others
who have searched for the same things have searched for.
For example, Joe searches for fried green tomatoes and
purple gummi worms. If Sam then searches for purple gummi
worms, then you might recommend he also look at fried green
Of course, this model doesn't work well if you only have a handful of
participants. But if you have many people searching you can say, based on
your analysis of previous searches, that if somebody searches for X, then
there is a high probability that he'll search for Y.
This is broadly known as Collaborative filtering.