There are various methods of doing this romanization. The most common method is one called the "Hepburn" method, but several other systems and variations are also in use. This has led to a confusing situation particularly with regard to people's names, where one name may be written in various ways in the roman alphabet.
There are three main systems of romanization. The "official" system is called Kunrei-shiki (訓令式) romanization. The most popular is Hepburn, hebon-shiki (ヘボン式) romanization, named after the compiler of a Japanese to English dictionary, J.C. Hepburn. This is less regular than the Kunrei romanization, but corresponds more closely to the usual English spelling of the sounds. The Hepburn romanization system is also called the hyōjun or "standard" system, even though it is not a generally-accepted system: MEXT wants everyone to use the Kunrei system. The third well-known system of romanization is Nippon-shiki (日本式), which has the advantage of a one-to-one correspondance between kana and rōmaji, whereas both the kunrei and Hepburn systems sometimes have the same romanization for two different kana in cases where the two kana are pronounced identically.
For example, the Nippon-shiki and the Kunrei systems romanize the tagyō as ta ti tu te to, whereas the Hepburn system romanizes it as ta chi tsu te to: the Hepburn system is less regular but is closer to the usual English spelling of the sounds.
Another common variant romanization system is the waapuro rōmaji used for computer input.
Several other romanization systems have also been proposed.