The dungeon master’s guide (the 2024 one) is a really great guide on how to run the game as a dungeon master, so the first thing I would recommend is just reading it, front to back. Which I know is a lot to read, but it’ll do a very comprehensive job of telling you what to expect, and introducing you to helpful techniques. If you do that, and you have the starter set, you should be able to run the game according to the instructions in the starter set. All the tools you need are already at your disposal, you just need to dive in and get some experience using them. If you have specific questions, this is a good place to ask them (though expect to get slightly different answers from everyone), but there’s no substitute for actual gameplay experience.
Regarding combat on a grid, if the idea is overwhelming or confusing for you right now, just don’t worry about it. The grid is entirely optional, you can run combat just fine by keeping it purely narrative, or by using small objects on the table as an approximate visual aid rather than precise measurements, or whatever you’re comfortable with. You can always try using a grid later, when you’ve gotten some experience and feel more confident in your skills as a DM.