Following the breakup of the Soviet Union, what are some of the major problems faced by many of the new countries?

Many of the new countries didn't know how to become democratic. The people weren't used to having a choice, voting, or political parties. Where they lived, the people had to fight to get to the top, often at someone else's expense. They were skilled at beating out competitors, but knew little about making friends.
The countries couldn't change their command economies to a free economy. Since the government no longer ran all policies and businesses, people had to learn how to run them for themselves.

How does this sound? Is my information correct?

Looks good.

Another problem was lack of money and a crumbling infrastructure.