In what ways did the US pursue imperialism in the 1890s? And how did the Spanish American war affect US foreign policy in the 20th century?

After the Spanish-American War, in which we inherited the Spanish colonies of Guam, Puerto Rico and the Philippines, we became the dominant empire in those regions of the world in terms of our military and economic control. 

Teddy Roosevelt, a veteran of the SA War, established the Roosevelt Corollary declaring the Caribbean essentially an "American lake" and taking a lot more direct interest and involvement in Central and South America.  He acquired the Panama Canal Zone and started construction of it as US territory.  These are areas and territories we would have to defend over the long term as an Empire.

Lastly, one of the reasons the Japanese attacked us at Perl Harbor and the Philippines was because our empire threatened theirs by our very presence in the region.  They simply wanted to remove the threat, especially in the Philippines, which we would not have been in at all if not for imperialism in the 1890s.