If during normal operation, I receive a mayday or pan-pan call, how should I handle this?
Am I required to provide help in this situation, and what can I do to make sure I give all the assistance needed, what information should I try and get?
If someone else is working with the station on the distress call, should I join in and help?
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.
As an addendum to the answer provided by Michael, there's also the point of what information to obtain from the distressed party.
If they're a "professional" or have otherwise had some sort of relevant training, they'll probably rattle off a whole checklist of bits for you to record and relay. Listen carefully, write fast, and read back to confirm all of their data points once they've finished talking.
If instead they're just someone with a radio, then you'll probably have to ask questions to direct their attention to the important details. Ideally you'll want to get the specific questions to ask from the emergency services you call. But depending on the circumstances, maintaining a three-way conversation may not be possible. So here are some important details you'll want to gather in pretty much every instance. Much of this is taken from aviation emergency handling, but applies in the general case as well:
What is the nature of the emergency - Plane crash? Hiking accident? Lost? Typically you won't have to ask, this is almost certainly going to be the first thing they tell you.
Who are you - Again, another obvious one, but getting an identity can help focus rescue efforts.
Where are you - You may have to ask for further clarification as they may assume you already know more than you do. Which state? Nearest city? Closest road? Landmarks? "What do you see?" If a search party is going to have to be sent, then the more detail you can get the better.
How many people are there - this is the "number of souls on board" question from maritime and aviation emergency handling. Most people won't even think to offer this detail, but it's one that every emergency responder will want to know. A head-count is invaluable, but if you can get it, a list of names is even better.
What are your intentions - Though most emergency advice boils to "stay where you are", you probably won't be in a position to make recommendations. But you can get an idea of what they are thinking. Find out their plan, their backup plan, and what they intend to do if that doesn't work out. While the individual may say "I intend to stay right here," it can be helpful to ask, "if you do leave, which direction do you think you'll you go?" Lots of rescue effort is spent on guessing people's backup plan.
What do you need - While you're not in a position to offer aid, it is helpful to get a list of their needs, so that rescuers can prepare accordingly. ("Alice has a broken leg and Tommie needs insulin")
You'll need to use your judgement to determine what to ask, or indeed whether you should ask any questions at all. As a rule, keep your communication clear but very brief. It's not uncommon for someone to have only a few moments to get a transmission out while being otherwise busy managing their emergency.
