Look up the address and phone number of your embassy or consulate in the country that you are staying in using the Internet. If you are on vacation and do not have your computer with you, most countries have some form of Internet cafe where you can cheaply use a computer. If you are in a real pinch, try asking a hotel for some assistance in locating your embassy's contact information.
Decide whether your issue requires a face-to-face visit or if it can be handled with a telephone call. For big things such as replacing your passport or reporting a birth abroad, you will need to physically visit the embassy, but if you just need some information and guidance from the embassy regarding issues such as medical care or adoption, then this can be done via the phone.
Physically and mentally prepare for your visit or phone call by having your passport or identification card (if applicable) and issue and/or questions ready to show and discuss. As a citizen, you will not have to make an appointment to visit the embassy or talk to an embassy official, but officials who work there are busy so it is best to be organized to make aiding you swift for both parties.