So sorry that you're going through this, sadly too many of us have.
You WILL get through this even if it doesn't feel like it right now.
Practical measures:
Legal advice ASAP for which you will need as much official "paperwork" as you can get your hands on. Marriage and birth certificates for you and DC, passports, financial statements, his salary information if you have it.
Others may disagree but I also highly recommend starting a claim with cms too. It will only get backdated to when you first claimed NOT to when he moved out, also my own life experience I've not come across an nrp yet who pays regularly and even the min amount UNLESS cms are handling it. He may still exploit loopholes but post here if so and mners can be great at helping.
If legally possible change the locks. I'm aware of several instances where exs have entered the former shared home when empty and taken valuables - including ones that were never theirs! Murder to prove and police generally don't like to get involved.
If you've a joint bank account take all the your money out then get it frozen and open a COMPLETELY separate account with a COMPLETELY separate bank (ie don't use a bank in the same banking group).
Do you work? Even if you do if you're on a low income for whatever reason get claims in for anything you might be eligible for ASAP. Again it's back dated to date of claim not when he left.
Emotionally/mentally
Tell the DC's school. It avoids them making any unwitting faux pas that may upset you and means the DC will get support if needed and the school then knows why if they're not themselves.
Sleep whenever and however you can. I couldn't face sleeping in the former marital bed and so slept on the sofa for first month or so after.
If eating is a struggle, keep it to light things or soups and supplement shakes. It can be easier to drink than eat with a lump in your throat and stomach in knots.
See your dr if you're really struggling.
Distract yourself - puzzles, talking to friends even just on phone, chatting here...
I recently caught a glimpse of exh on FB and barely recognised him! He's married ow, they've had 5 DC and I have it on good authority they're both utterly miserable! He's cheated on her too several times. Well, you reap what you sow.