GlobalCountryCode.org is your comprehensive resource to help you make calls anywhere across the globe. This page details how to dial Japan from Singapore.
To call Japan from Singapore, dial 001 + 81 + the number you wish to connect to.
Most mobile phones and smart phones have the "+" sign on the same key as "0". To call internationally from most mobile or smart phones simply dial the "+" sign, followed by the country code, city code and local phone number as shown above.
TIP: If you travel abroad often, save all the numbers in your contacts with the "+" sign. The sign will be ignored when you're at home but will save you the hassle of redialing numbers when you're abroad.