How did the American colonies win their freedom in the American Revolution?

They fought against the British!

http://en.wikipedia.org/wiki/American_Revolution

The British gave up and sailed home.

For more details, check this article.

http://en.wikipedia.org/wiki/American_Revolution#The_war_winds_down

The American colonies won their freedom in the American Revolution through a combination of various factors, including military strategy, international support, and political and ideological developments. Let's break down how each of these factors contributed to their victory:

1. Military strategy: The colonies adopted guerilla warfare tactics, which allowed them to effectively resist British forces. They utilized their knowledge of the local terrain and employed hit-and-run tactics, making it difficult for the British to engage them in traditional open-field battles. Additionally, the leadership of figures like George Washington, who provided strategic guidance and fostered resilience among the colonial forces, played a crucial role in The Continental Army's success.

2. International support: The colonies received assistance from other countries, most notably France, who provided military support, supplies, and naval forces. France's involvement, motivated by their desire to weaken their long-time rival Britain, proved instrumental in tipping the balance in favor of the colonists. The American victory at the Battle of Saratoga in 1777, which showcased the strength of the colonial forces, played a crucial role in convincing France to form an alliance with the colonies.

3. Political and ideological developments: The American Revolution was driven by a desire for independence and the idea of self-governance. Influential writings, such as Thomas Paine's pamphlet "Common Sense," which argued for American independence from Britain, helped shape public opinion and ignite a spirit of rebellion among the colonists. Politically, the Continental Congress united the colonies and provided a central authority to coordinate their efforts, including the establishment of an army and the negotiation of alliances.

It is also worth noting that the British faced challenges in maintaining control over a vast territory far from their home base. Supply lines and communication were often difficult, while colonial knowledge of the local environment and support from the local population further hampered British efforts.

The American Revolution was not won solely by one factor but rather through a combination of military strategies, international support, and political and ideological developments. These elements worked in tandem to weaken the British position and ultimately secure victory for the American colonies.