What are enacted to limit the amount of goods allowed into a country? Quotas? Sanctions? Tariffs? Free trade agreements?

Sanctions, quotas and tariffs all seek to restrict the movement of goods into a country.  Free trade agreements encourage the import and export of goods between member countries.
Sanctions are penalties imposed upon one country by either a single country (unilateral) or multiple countries (multilateral).  The sanction is a formal notice to a country that imports and/or exports will be tightly controlled until the penalized country meets a specific demand such as ending genocide.
Quotas are restrictions on the quantity of items or the value of items accepted for import.  They may be part of a formal sanction or a standard restriction to trade.  The goal of quotas is to protect the domestic industry from a flood of foreign product.  Quotas can also control prices by keeping supply low during high demand periods.
Tariffs are a tax imposed upon import goods.  Importers must either absorb the tax, reducing profit, or pass it along to consumers, increasing the market price of the good.  The increased cost may make it less desirable to the public, thereby limiting market share.  Tariffs are designed to control domestic prices and employment by making the market hostile to foreign entries. 
Free Trade Agreements (FTA) reduce the restrictions on importing goods to a foreign market.  FTAs allow for a more global market place and access to a greater number of products by allowing exporters a low-cost method of placing goods in a variety of regional markets.  Detractors argue FTAs also reduce employment and encourage counterfeit goods.