There are various methods of restricting trade that include imposing trade barriers and/or quotas and imposing tariffs. Tariffs act like an extra tax or fee on the product that generally makes it more expensive to purchase. Trade barriers and/or quotas restrict the numbers of units of a product that can be imported into the market.

For instance, China has long had a policy of restricting the number of Hollywood produced films that it would allow into China to play in domestic movie theaters. Over the years, the US film industry has lobbied China to open trade up so that a greater number of Hollywood films could be shown in the country. China has responded by increasing the number, but the country continues to impose a trade quota on Hollywood titles.

In some cases, a market imposes trade barriers that bar the product entirely so that no units can come into the market legally. For example, the alcoholic beverage absinthe is prohibited from being imported into the US because it is deemed potentially harmful to drink. Another product that has been prohibited from importation into the US is a chocolate egg, Kinder eggs, which have been banned because there is a small toy contained within the cavity of the egg and concern that small children could consume the egg, toy and all, and choke. The manufacturer of Kinder eggs sells a version of the product specially produced for the US market that is FDA compliant.

Nations use trade restrictions as a matter of both foreign and economic policy. A nation can blockade another nation in time of war—this restricts all trade going in and out of a country. A nation can also use trade sanctions in order to punish certain industries. One example of this is when the United States would not sell high-octane fuel to Japan during World War II.

A nation can also use embargoes to limit trade. One key example of this happened when President Jefferson levied an embargo against belligerents during his administration. This embargo backfired, as key European nations also did not buy American goods, thus crippling the US economy.

Tariffs are a key part of economic policy. Tariffs are taxes placed on imports. They are used to protect industries in the home country. Tariffs often become political issues, as interest groups want their industries protected. When another nation issues tariffs in retaliation, a trade war results. Tariffs also increase the price of foreign-made goods, thus hurting the consumer as well.

Nations can also issue quotas to ensure that other nations do not dump excess product there, thus lowering the prices. A nation can state that only a certain amount of product can be imported, with the remainder being made up of domestic goods. Once again, this is done to protect industries at home.

Nations also use most-favored nation status when referring to trade partners. Such nations are given precedence, at the cost of alienating other nations. Nations can also form cartels, like OPEC, in order to control the global price of raw materials.

There are a number of reasons why a nation might want to put limits on trade in spite of the economic positives of international trade. The methods that they can use vary, but common methods include the use of the following:

Quotas can be instituted to limit the quantity of a certain product that can be imported. This can be done to leave room for the domestic market to produce the same good and drive up the price of the product.

Standards can have the effect of restricting trade. By making requirements that an imported good must meet certain health, safety, or quality standards, a country can prevent certain exporting nations from trading the good.

Tariffs are taxes on imports. By placing tariffs on certain goods, it may no longer make economic sense for a country to import that product. This sometimes leads to the exporting nations of that product to implement their own retaliatory tariffs on the goods they import from the country that instituted the first tariff.

Embargos can be implemented in extreme situations. An embargo ends all trade of a certain good from a particular country. In some cases, an embargo can be used to stop all trade with a country. This is usually done to put economic and political pressure on another country.

I would say that there are three general types of trade barriers (methods of restricting trade between countries).  These are quotas, tariffs, and regulations.

A quota is a law that limits the amount of a certain good that can be imported into a country.  It says, for example, that only X number of cars can be imported into the US in a given year.

A tariff is a tax on imports.  This raises the price of the imported good and makes it relatively more appealing to buy domestic goods.

Regulations are rules about the imports themselves.  They are not supposed to be made with the purpose of restricting trade, but they often are.  An example of this would be South Korean rules about beef.  These are supposedly meant to prevent mad cow disease but are mostly used for limiting imports of US beef.  So these are rules that are ostensibly not about trade but they end up being used to restrict trade.