How might computers contribute to unemployment in modern society?

In the short term, computers can contribute to unemployment, but this effect should disappear in the long term.

The main way that computers can cause unemployment is if they make certain people's jobs unnecessary.  For example, firms used to employ large numbers of stenographers and typists.  Computers have made these people unnecessary.

Computers can also cause unemployment in certain countries.  For example, the rise of the internet means, for example, that an American who specialized in typing up medical records could be replaced by a lower-cost individual in another country.  The records could be transmitted by the internet.

Economic theory suggests that this is good in the long term.  Computers will open up new job categories even as they close some jobs off.  For an example of how this worked historically, think of the change from horses to cars.  This put many people out of work (saddle makers, for instance) but opened up many new kinds of jobs.