How did the American tariff policy slightly cause the Great Depression to occur?

The US tariff policy didn't cause the Depression to start
since the Smoot-Hawley Tariff was not passed until 1930.  However, the tariff did help
to make the Depression worse.  This was because it helped to cut down on the amount of
trade going on between countries.

After the US enacted this
tariff, the governments of Canada and Great Britain, among others, enacted tariffs of
their own.  These may or may not have been in retaliation for the US tariff.  One way or
another, the tariffs' cumulative impact was considerable.  As the "salem-history" link
below says,

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The League of Nations estimated that the volume
of world trade declined in real terms by more than 65 percent between 1929 and
1933.

The US tariff policy
helped to cause this because it helped to make it less profitable for nations to trade
with each other and because it helped make other countries impose their own tariffs. 
These tariffs, and the reduction of trade that they caused, helped to deepen the
Depression.