The United States acquired Hawai'i through economic and military power.
The economic power came with American domination of the islands' sugar industry. Americans brought this industry to the islands and came to dominate it completely. This gave Americans a huge stake in what happened to the islands as well as power to impact the islands' future. The military power came because of America's superior resources and technology.
The two types of power converged to take Hawai'i from its native people late in the 1800s. The Hawai'ian monarchy was overthrown by wealthy Americans such as Sanford Dole with the help of the US military. Once this was accomplished, the islands were eventually annexed by the United States.