The Rough Riders became famous for their bravery against the Spanish in Cuba. Though the Riders and Roosevelt in particular gained much publicity for their especially daring assault of San Juan Hill, they probably could not have done it without support from a black regiment, which recieved relatively little publicity.
The publicity he earned with the Rough Riders helped to elect him as Governor of New York 1899.
In 1900, he was made Vice-President under William McKinley. When McKinley was assassinated, Roosevelt took over.
His presidency is remembered as a time of monoply-busting and industry reform. He was elected in 1904 and probably could have won again had he chosen to run.
When a revolt broke out in Cuba in 1906, Theodore Roosevelt used his Roosevelt Corollary, which declared his intentions to send troops to countries he deemed uncivilized, to justify sending troops to Cuba. This began a second American occupation of Cuba from 1906 to 1909.
Roosevelt ran for the Presidency with the Progressive (Bull Mouse) Party in 1912. He lost, and disappeared from politics. He was 60 in 1919 when he died in his sleep.