My xH drove off to a saturday morning meeting two months ago and just didn't come back afterwards, instead went to his parents' house and I found out by text (from his dad) the next day. It is the best thing to ever happen to me. It was such a relief, like a big heavy weight had been lifted off me and I feel alive again.
As for advice. Depends really. Do you mean emotional, financial, ..?
I would suggest the first thing you do is call up the citizens advice bureau and make an appointment to talk to someone there. They will be a good starting point for advice. I would also find out about a divorce lawyer, just so you get the correct advice regarding finances too. If you have a joint bank account and are in any way concerned about that, call them and get it frozen.
The kids need to be told as soon as possible and in a clear, honest way without any emotions.
You need to call people (friends, family) get yourself emotional support and a break from the kids. If you are working take a day or two off to gather yourself. What felt good for me was moving his things out of the house and into the attic, so I wasn't staring at it all day. Take time to think about all the things you have sacrificed in the relationship. For me, spending some time and a small amount of money buying some new clothes, make up, eating the dinners I like, chatting and reconnecting to people on the phone and meeting up, planning my future - has all helped. If you think it will be emotionally difficult for you, there is nothing wrong with getting some professional help from a therapist to help you through this. And take all the time you need, nothing needs to be done immediately (barring the CAB/lawyer/bank bit).
He will (most likely) irritate you, mess the kids about, not call them when he says, not see them for weeks on end, mess you about emotionally/financially. But you are in control and don't need to let any of it get to you.