Citizens of Western Europe, the USA and Commonwealth countries don't need a visa to enter Singapore. Check with the relevant embassy before departure . Unless you specify how long you intend staying, you'll normally be stamped in for fourteen days .
Extending your visa for up to three months is possible, at the discretion of the Singapore Immigration and Registration Department (Mon-Fri 9am-5pm; tel 3916100). Extensions beyond three months are less common, but there's always the option of taking a bus up to Johor Bahru, across the border in Malaysia, and then coming back in again.