(TLDR version: Become a leader. The rest is just adaptation and experience.)
Great answers already about bringing your own knives (buy a knife roll/bag) and maybe even extra things, especially for the dishes you plan to make. I've also stocked up at least 3 people's kitchens with things they didn't have because I cooked there frequently enough. Yeah, I'm out a few hundred bucks, but my holiday stress level is reduced. By that same token, try to bring anything that's important for your dishes, especially if you're not sure about what the host keeps around -- your set of spices/herbs is a big thing is often forgotten when packing your ingredients.
However, the biggest advice I can give you is to become the respected cooking expert in the group. If you take a serious role in helping plan and execute the major part of the meal, just letting others volunteer to bring pre-prepared dishes -- i.e. they won't be in the kitchen -- and you become the "problem solver" for the cooking, over a couple of years, you will start to take on the role of the kitchen leader, and others will defer to you. Pretty much every kitchen you walk into where the meal was planned with you will become your kitchen for the day. If you're lucky enough to have someone in-the-know with a good sarcastic streak helping, you might even get the occasional mocking "YES, CHEF!" to let you know when you're getting a little too bossy and forgetting to say "please" and "thank you".
Note that you don't get here through a hissy fit or power play. This requires actual leadership skill on top of having a passion for cooking and being willing to take responsibility for the success of the meal. It also means you're taking on the stress of it, but you're doing it because you like it. This is exactly why this method works; people like to follow a confident leader and let them take responsibility. If someone else is running the kitchen, then just remember that it's their stress, not yours, and you're just there to help them as best you can, so don't sweat the small stuff.
Once you've moved into the kitchen leader role, you'll probably find that people will not just invite themselves into your kitchen (that's rude). They will volunteer with "is there anything I can help with?" Since you should now be aware of everything going on in your kitchen and what needs to happen, you should always be prepared to answer this question. If there's nothing at the moment, then defer to the host to see if they need anything done not in the kitchen. But also realize that now you can control the kitchen traffic. For instance, "Yeah, actually, I could really use someone to prep these Brussels sprouts. Here's a paring knife and a couple of bowls; there's more space at the table if you want to sit there and do it." It's also OK to say "not at the moment, but check with me again in 20 minutes".
And as Joe mentioned, try to keep someone who lives there nearby to help find things. They may be your "sous" for the day, or they may not even be much of a cook themselves. I would go a step further by pre-gaming the cook with your main "crew" and asking for the location of major items you will need. If there's room, maybe even do a little supply mise en place so you can just go to your "supply station" instead of remembering. Call out for things while you're finishing tasks and let your "assistant(s)" locate them for you. Do all your sink-centric prep work early, then let a volunteer help clean dishes and clear away the mess while you and the other cooks focus on cooking. You'll definitely need that big bowl again, and someone at the sink won't be in the way too much.
Source: Experience. I run every home kitchen I walk into now by default. It helps that I'm also comfortable in a leadership role in general, so this is not just a kitchen thing for me. If I'm not the head cook for the day, I'll drop by the kitchen as I'm unloading anything I brought and just let them know, "Hey guys, I'm here, give me a shout if you need anything." Usually, I just enjoy myself and let them work. Frequently, I will be called in to taste-test, so at most it's just suggesting a pinch more salt or a splash of vinegar to brighten the gravy, or saying "I think it's good!". Sometimes I may get called in to troubleshoot, at which point I usually become the de facto leader again. This means I need to be conscious of the whole kitchen, especially because the overwhelmed head cook is now worried about this failing dish. So if it's taking a while, I may have to say, "I've got this for now if you need to check on your other food" to remind them. Once I'm done helping with that, I step out and let the cook take over again. I'll come back and check on them to make sure they're still good, but otherwise stay out of the way unless they request me. If I do get asked to stick around, I often have to remind them that it's their meal and I'm just helping, because people will instinctually expect me to take charge. So be aware of that, too -- once a leader, always a leader, even when you're in the follower role that day.