Excellent thread! A CCR friend of mine and his regular diving buddy (who is on OC) put together a lecture on this a few years ago, I'll see if they have it online anywhere. I frequently dive in mixed teams. As rebreathers become more and more common, with vacation dive destinations starting to cater to them, it's more an more likely that the average OC diver will run into one.
One thing to know about CCR divers is that we love to talk about our rebreathers, at all times EXCEPT during our pre-dive checks. If you see a diver breathing through the loop on the dive boat, don't ask them questions, and if you do, don't assume they are rude if they don't answer. Even apart from the pre-breathe, there are a number of things on the checklist that we may be going over, and that's not the time to be chatty.
I usually show my OC buddies where my ADV (automatic diluent valve) is. I tell them that if anything looks "funny" to them, I won't mind if they push that button to give me a shot of fresh gas of a known composition, preferably while holding my mouthpiece in place. Unless I have hypoxic dil (which I don't use), the diluent will always be safe to breath at any point in the dive, and exchanging the gas in the loop with diluent might be a helpful first step in dealing with any gas related issue.
If it's just me and a single OC diver, then we need to talk about what to do in case they need gas. CCR divers all carry bailout, which is basically a complete OC scuba unit (tank and regulator) that is usually set up for immediate deployment. This usually looks like a tank hanging in the usual slung position on the divers side (I carry an 80, but sidemount style). However, be aware that there are some less common rebreather configurations where the diluent and the bailout are both backmounted, or even the same tank. Don't be afraid to ask (as long as the pre-dive check isn't happening!).
With a rebreather, the danger isn't so much running out of gas as it is breathing the wrong gas - too much or too little O2, or too much CO2. A diver with hypercapnea (too much CO2 in the loop) has symptoms that can make it very hard to switch to that backup system, so we make it as easy as possible. Some people have a bailout valve, in which case the rebreather mouthpiece can be switched to either connect to the loop or to the OC regulator. This is also something that an OC buddy could potentially switch if the CCR diver was unresponsive. Others (like me) have a separate OC regulator bungeed underneath their chin. Still others just have their OC regulator bungeed to the bailout tank (I don't like this).
So what do we do if you, the OC diver, needs gas? Well, you could take the bungeed necklace, although I don't like the idea of me then having no bailout, so that's not ideal. What I have done in some cases is put a second OC regulator on a long hose on my bailout regulator. In this case, I want to be sure that it doesn't accidentally free flow without me noticing it, so I put a shutoff valve in the line. And for a diver carrying more than one bailout tank (some divers carry 100% O2 for faster bailout decompression), it's obviously crucial to breathe from the right tank. As you can see, it's important to thoroughly discuss whatever the OOG plan will be ahead of time.
You might want to know what that flashing red light on your new CCR buddy's handset means, so ask. Usually, that means that the oxygen levels are too low or too high. There have been cases where the buddy noticed this before the diver did, and called his attention to it! Not the way it's supposed to work, but a good thing to know.
It's not a bad idea for the OC diver to figure out where the wing inflator is, in case a rescue is necessary. Also, we usually do a bubble check at around 20 feet on descent. Something to talk about ahead of time, but small bubbles on a CCR can be more of an issue later in the dive than on OC, so we always check for that on the way down. Do us a favor and look for bubbles that we can't see.
Finally, one thing that CCR divers don't like is a sawtooth (up and down) dive profile. We much prefer to swim around things than over them. That's because unlike OC, every ascent requires venting gas from the loop, and every descent requires adding gas from a very small tank. Also, up and down motion causes the PO2 to drop and spike, respectively, so we try to minimize that.
I’m probably forgetting some things here, but that’s a start!