First, if you hear a distress call: STOP! Immediately end any transmission in progress. Do not touch any antenna or radio controls except as needed to turn off split operation etc. Lock the VFO to avoid inadvertantly bumping the frequency setting. Particularly, do not reorient the antenna in an attempt to get a better signal. Focus on copying what you can and avoiding any activities that may cause interference. This is something you can actually practice: how long does it take you to reset RIT, turn off split, lock the VFO and getting ready to actually write things down?
Then, I view it as a multiple steps process.
Copy the message. You will not remember the details. Write down everything, clearly marking anything you are not absolutely certain about. This is a major reason why I feel one should always have writing utensils within easy reach from one's operating location; the odds that you'd receive a distress call are small, but if you do, any old pencil and back of a log book page will help tremendously.
Wait to see if a station better equipped to handle the distress call responds. Maybe there's someone closer, or with necessary knowledge (for example, there's the possibility that a doctor hears a distress call that is about a medical emergency).
If nobody answers within a few seconds (and you are sure that nobody does and you aren't simply out of range of the other station), briefly identify yourself and then stop transmitting again. This might be something as simple as "amateur radio station VK2VXK received distress call - distressed station please confirm, over over". Your transmission lets anyone within range of you but out of range of the distressed station know that the frequency is in use for emergency traffic (a definite signal to cease transmissions), and if you get a confirmation from the remote station you have established two-way communications. I'd use the remote station's call sign if they gave one, but don't worry if they didn't. In many jurisdictions, emergency communications is allowed on any frequency unlicensed if needed to solicit help. In many jurisdictions this also means that you can respond to a distress call even if you are normally not authorized to transmit on the frequency in question, if doing so is necessary to provide emergency assistance.
As soon as you have "claimed" the distress signal by receiving confirmation from the remote station, tell the remote station to stand by and pick up the phone and call emergency services. Immediately inform them that you have received a distress call over radio (so that they do not rely on locating your phone line to determine the location of the emergency), and accurately relay all information in the distress call. Particularly important are the type of emergency, how many people are involved, and the distressed party's location. Be prepared to relay questions and answers between the emergency operator and the distressed station. Stay calm (easier said than done, but very important). Maintain communications with both parties until you receive confirmation that emergency services have arrived. If you hear anyone transmitting on the frequency, immediately calmly inform them that the frequency is in use for emergency distress traffic.
If someone else has already established communications with the distressed station, then do not interfere. Also, do not play radio cop. If some other station starts transmitting on the frequency, let either of those already communicating deal with it. Instead, simply copy all details you can, stay on the frequency and do your best to be prepared to jump in if either of the stations ask for assistance which you are able to provide or the station that is in communication with the distressed station clearly goes off the air, but not under any other circumstances.
I doubt you would be legally required to provide assistance to a distressed station, but if it was me, I would sleep considerably better at night knowing I did whatever I could to help, even if it was something as simple as ceding a frequency to a station in distress. Actual emergency or distress communications always has precedence over all other communications.