Sentosa is one destination where getting there really can be half the fun. For a grand entrance and overview of the whole island, take a taxi to the Mount Faber cable car terminus and take the aerial tram across to the island. The cable car sets you down in the middle of Sentosa, so it's a great way to go, although also the most expensive, at S$24 (15.18 USD) per person.
If you're looking for a cheaper way, or just afraid of heights, then take the North-East ("purple") MRT line all the way to the Harbourfront station. From there, you can also catch the cable car, or look for the orange Sentosa buses at the bus interchange, or you can catch the Sentosa Express monorail from the Vivo City shopping mall. The bus costs S$2 (1.27 USD) per person while the monorail is S$3 (1.90 USD) per person.