Explain the roles and actions of different levels of government in relation to trade.

I am assuming that your question is about United States government and relates to international trade, not trade within the United States.  The only level of government that has control over the United States trade with foreign nations is the federal government, as mandated by the Constitution. Other levels of government have no power at all. 
Article I, Section 8 states that Congress regulates commerce with other countries.  There are a few different options that can be exercised in foreign trade.  One is to impose a tariff on in-coming goods, which makes them more expensive for Americans to buy, thus encouraging people to buy American-made goods instead.  This runs the risk of other nations doing the same, which means that fewer people will buy American-made goods. Another option is to have no tariff at all, which is pure "free trade," so that goods move freely over borders without any taxation.  Finally, an embargo can be imposed, which is generally done for political reasons, although one could certainly be imposed for a situation in which unsafe products from other countries were being sold.  We have had an embargo against Cuban products for a very long time. And while no one discusses this, I am sure that we are not supposed to be purchasing any goods from North Korea.
State and local governments are not permitted to enter into trade agreements with foreign countries, and it is easy to see why.  It would destroy the cohesion of the country.  If New York had a trade agreement with France, and Pennsylvania imposed tariffs upon French goods, it would be a disaster.  French goods would be routinely smuggled from New York to Pennsylvania. And that is just one small example.  To be a nation, there must be one cohesive policy that covers all the states. 
None of this stops anyone in any state from selling to or buying from other countries. It simply means that whatever rules apply to the situation, they have been decided upon by Congress, and they apply to all the states.