Start working on a MUCH larger brooder ASAP. They are going to outgrow that box very quickly!
I would make a "baby bottle" style waterer to help keep their new brooder dry. I made one for about $6 with a sports bottle I picked up at Aldi and a horizontal nipple.
Keep them on a good chick starter and offer a separate container they cannot flip over with chick grit.
Once they are in their new larger brooder, you can give them plugs of sod from the soil the coop and run are in to acclimate them to the microbes they will be exposed to.
Check them multiple times a day for pasty butt.
Make sure that the brooder is not too hot. Only one side should have the heat source and the other side should be much cooler and where the food and water are kept.
Good luck with your new chicks!
Oh, and if my comment about the sod of plug coming from the area where the coop and run are didn't make it's point, your coop and run better be ready for them or you will be seriously scrambling to get them a proper home!
That's too broad a question so I'll suggest you go to the Articles tab at the top of this page and read articles in the Learning Center. That will keep me from typing all day. And read several articles, you will find that we all do things differently. More information about your brooder and how you are managing them could spark specific suggestions that apply to your situation. For instance, I'd put more rocks is that water dish so they can walk on top better.
The basics are to keep your brooder dry and don't overheat or chill your chicks. Provide appropriate food and clean water. I don't know how you are providing heat for those chicks or whether your brooder is inside in a climate controlled area or outside with widely varying temperatures. My ideal brooder keeps one area warm enough in the coolest conditions and cool enough in the warmest conditions. Inside your house that can be pretty easy to do. Outside it can be more challenging.