Most places will search a range of years, frequently five, for a certificate that matches the details you specify, and supply you with a copy if a match is found. Civil registration certificates can be obtained from the relevant registering authority. This is frequently the government statist in the area of the event. In Australia, the relevant authority is in the capital city of the state in which the event occurred. Addresses for these can be found under the appropriate state in the addresses section of the Australian Family History Compendium.
Some indexes also contain information such as parents' names and birth place.
When you find an entry that appears to be relevant to you, you can quote the registration number to receive a copy of that certificate. Some places will supply the certificate at a reduced price if the registration number is quoted. Civil registration indexes can often be found in municipal and state libraries. In many cases, indexes can be purchased. Before the start of civil registration, the local minister of religion was responsible for recording baptism, marriage and burial events.