The world of Imperialism consists of provinces ruled by governors. To win you must obtain the support of a majority of governors.
The world-wide Council of Governors nominates two Great Powers for possible victory every 10 years. To be nominated your country must expand its industry and economic clout. Once there are two nominees all the governors in the world vote for one of the two, or abstain from voting.
Owning, conquering or colonizing a province provides automatic support if your country is nominated to win.
If your country is nominated, governors in other countries may choose to support you due to your diplomatic or military successes. Generally, provinces owned by Great Powers consider military threat when deciding to vote. Minor Nation owned provinces, on the other hand, are more interested in the diplomatic prestige of the nominated Great Powers.
You might choose to play aggressively in one area of the world, and peacefully in another. A combination of military and diplomatic strategies will generally garner support the most quickly.