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Some "first past the post" defenders say that proportional representation encourages the formation of smaller parties and thus, minority governments.  How does this happen?

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It is definitely correct to say that first past the post (FTPT) systems discourage the creation of small parties while proportional representation (PR) systems encourage small parties.  This is because it is much easier for a small party to get represented in a legislature under a PR system.

In a FTPT system like that in the United States, Canada, and the UK, it is hard to have small parties.  If a party wins 30% of the vote, for example, it gains no seats in the legislature unless that is a plurality of the vote.  Therefore, it is very difficult for small parties to arise as they must get to the point of being able to win pluralities in various districts before they can have any representation in the legislature.

By contrast, PR systems allow small parties to get representation.  For example, a party that won 20% of the vote would get 20% of the seats in the legislature even if they did not win a plurality in a given district.  This encourages small parties to form because they can actually win seats in the legislature.  As more small parties come to exist, there is a greater chance that the party that has the most seats in the legislature will not have an outright majority and will need to govern either as a minority government or in a coalition.

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