Having DM'd for a group that fluctuates between 6 and 10 regular players for almost 2 years now, I've learned a few important things:
-When dealing with a larger than average group, don't be afraid to say "alright, and now we're gonna move over to these characters for a bit and find out what they're doing". Time dilation is a thing in fiction and it can be a thing in D&D as well. This helps prevent some characters from hogging the spotlight. It's not the most elegant solution, since it has players sitting out for a while, but it's a solution that works particularly well for when part of the group is in combat and the other part isn't.
-If you do have a character that seems to be hogging the spotlight (it won't usually happen on purpose, it just happens sometimes), try to find a way to let the rest of the group or neglected characters shine. Maybe a roleplay moment, or a situation that specifically requires their skill set.
-Don't plan too much. Planning is important, but try to keep those plans flexible. Create your world, create your Main Problem, and make a bunch of smaller problems leading up to that Main Problem. Figuring out a solution to those problems (or ignoring said problems entirely) is up to your players. Common sense prevails from that point on. Did your players not bite that plot hook of a magical plague bringing a city to it's knees? Maybe next time they pass by the city has a drastically reduced population or NO population.
-Don't be afraid to say yes. If you have a player who wants to try and do a leaping Cleave from one gargantuan psychic nightmare worm to another, by all means let him give it a go. That doesn't mean he'll actually SUCCEED, but you at least let him try. He might roll really well and pull it off!
-Don't be afraid to say no either. According to the rules, a character technically has an unlimited amount of free actions per turn. Free actions include things like talking and other incredibly minor actions that require no real thought to perform. That being said, a person can reasonably only snap their fingers/shout out a sentence/fart a certain number of times in a 6 second window. If you feel rules are being abused, lay down your law.
-Do not coddle your players. Everyone showed up to have fun, yes, but it's hard to feel excitement or tension when your players start to think that they can get away with anything. It's alright to fudge dice rolls once in a while, like if you don't want to straight up murder the wizard in a surprise round before initiative is actually rolled, but most of the time I've found it's good policy to let the dice land how they may. If the dice say you're dead, then sorry, but that's the game sometimes.
-If there are any powerful people/creatures of note in your world, consider having stat blocks for these characters prepared ahead of time, juuuust in case.
-Having a general "town guard" template stat block is very useful. Swap gear and feats around as appropriate for the area and you're good to go.
-Learn from your players! I freely admit to not having as good of a grasp on the rules as I should. If your players draw your attention to something that you've been ruling incorrectly (like my totally goofing on how the saves for the Phantasmal Killer spell work), then take note. Everyone having a good time is the most important thing, so while your ruling as DM is final, that doesn't mean you're always right.
-Something that I will do for my next campaign, create a pre-rolled stat array for people to use. This eliminates any glaring power-gaps in regards to character stats, and also allows you to pace the game more how you would like. For example, if you want your players to be a group made up of total badasses give them a stat array of 18/16/14/12/10/10. They put those stats wherever they like, and no one is left desperately trying to keep up with people who just rolled better stats than them.