The French and Indian War was just part of the continuing struggle between France and Great Britain for control of North America, and was the fourth war over this issue. France claimed basically all of North America and vast areas of the Caribbean, except for the vaguely defined British colonies along the East coast of the continent and a few areas still owned by Spain. France derived profit from merchandise sold to its colonies and Native Americans, and a trade in furs from the New World. Britain and its colonies wanted more space for expansion and security from both Native populations and the Catholic French (the colonists being largely Protestant).
The immediate cause of the war was the question of who owned the "Ohio country", claimed by France and the colony of Virginia. The ambush of a party of French soldiers and Iroquois warriors by a small Virginia party under the control of a young officer named George Washington was the initial combat of the war, and the alleged "assasination" of Sire Jumonville de Villiers, the French leader, was the actual political cause of the war.
The Battle of the Monangahela was a disastrous defeat for Britain, Gen. Braddock being killed and the army saved only through the action of Washington and the colonial troops. There were many battles, including French victories under the command of Montcalm at Fort Oswego and Fort William Henry, and a failed British expedition to take Louisbourg.
All defeats were redeemed by Wolfe's success in taking Quebec September 13, 1759. When the remnants of the French forces approached from Montreal they were beaten at Sainte-Foy on September 28, but the British retreated back into the city. The French besieged them, but had little ammunition, and the war essentially ended when British warships arrived on May 15.
The effects of the war included the expulsion of French settlers from Nova Scotia and the final defeat of French hopes for an American empire. It also left the British with the need to station a great many more troops in America to protect the much larger frontier, but without increased revenue to pay for the expense. This led to succesive British governments attempts to raise more money in taxes from the colonies to help pay these expenses. New taxes were invented, which caused discontent; more soldiers were stationed in the colonies, which also caused discontent. Finally, many taxes on imports were reduced, but in the past most tariffs were not actually collected. Lowererates but more enforcement would cost merchants more, and the smaller merchants couldn't afford this. The larger traders (and smugglers), such as John Hancock and Benedict Arnold, did not want to pay. This was the beginning of the agitation which eventually led to the American Revolution.
Of course, the French and Indian War was the initial cause and the New World campaigns of what is termed in Europe the Seven Years War, which also involved a struggle between Prussia and Austria for control of the Germanic states.