What was the official policy of the USA on colonisation? How well did America follow it officially and non-officially? What were the reasons behind it?
Well technically they colonised the rest of the country. Initially the USA was only the eastern seabord.
The United States did not have an official colonial policy, however, the US had colonial aspirations that probably date back to the idea of "Manifest Destiny." This starting point is problematic though because typical colonial powers sought to utilize the local populace in some manner (as a captive market, extracting resources, etc.) whereas the US wanted to extend to California and get rid of all the inhabitants.
It was not until the right before the Spanish-American War that the United States began to develop a thirst for typical colonies akin to the European nations. As Professor Thomas McCormick articulated in this article from 1963, the purpose of the US territorial expansion was to keep foreign markets open. Professor McCormick's article is heavily sourced with quotations from administration officials around the time of the Spanish-American War stating their concern for the free flow of American commerce.
Part of this desire to keep markets open for US goods was the desire to be considered a world power. One way this was expressed was in Theodore Roosevelt launching his "white fleet" to impress domestic/international audiences. Swept into this thinking was also a sense of "mission" not dissimilar to the idea of "white man's burden," to bring civilization to the rest of the world. This theme (and the others touched on) is discussed in Mary Ann Heiss's great article The Evolution of the Imperial Idea and US National Identity
So, the US colonial policy was really to keep the rest of the world open for US business, and as a secondary goal, civilize the rest of the world. That policy has not changed terribly much to this present day.
Well other than territories taken from the Spanish American war, and Hawaii, America never went on a sort of "colony" building expedition like the Europeans. There was plenty of land here to take over rather than go to other countries, which were either already claimed or in the process thereof by other countries. Still the fact remained we had more land here to inhabit than was possible to fill during most of the 19th Century so we didn't need to look far, except for maybe Mexico...
Some places to look for information is on the Colonization of the Philippines, which notes on the first page the feelings towards a US colonial empire - http://www.jstor.org/pss/20067365
Texas, could be considered a colonization effort since it was initially part of Mexico - http://www.tshaonline.org/handbook/online/articles/uma01
And for some reverse colonization you can look at the American Colonization Society that wanted to put free blacks back in Africa - http://en.wikipedia.org/wiki/American_Colonization_Society