Suppose a firm that manufactures aluminium is emitting large amounts of pollution into the air. Suggest ways in which the government can deal with...

One way that the government could deal with this would be
to simply mandate that the company reduce its emissions of the pollutants to a given
level that the government feels is acceptable.  The company would then be free to
determine how it wished to go about reducing the
emissions.

Second, the government could decide exactly how
it wanted the pollution to be reduced.  It could then order that the company take those
particular steps.  In this case, the company's role would be to install whatever
equipment the government told them to install.

Finally, the
government could require the company to pay for the estimated costs of the pollution. 
This would mean that the true price of the aluminum would be accounted for because the
company's costs would go up (there would no longer be externalities).  The company would
then determine whether it was more practical to continue to pay for the costs of the
pollution or to take steps on its own to reduce it.