Hi!
I think "Foundation" is a term used in England and Wales, so I assume you are in one of those countries? In order to start out, you need to send a deregistration letter to the school your older children attend. Without that, their names cannot be removed from the register and so you'd get into trouble over truancy if you just stopped sending them. If they are at a mainstream school, it's as simple as that. There is no notice period and you don't need approval. (Children at a special school do need the LA's consent for deregistration, but this should be a formality.) They are then officially home educated, and you have great freedom in deciding how to go about it. In the case of your youngest, you simply don't register him/her at a school in the first place, and you don't have to inform anybody that you intend to home educate.
The Local Authority has a duty to intervene if they have reason to believe that a child in their area is not receiving a suitable education. LAs vary widely as to how they interpret this. Some are quite pushy about wanting to have regular "inspections" of all families, a policy which is in clear breach of government guidance. It is a postcode lottery. The government guidance to LAs in England is clear and useful: I'd advise you to read it so you know what the score is. If and when your LA gets in touch, feel free to post on here to ask whether you have to do whatever it is they are asking you to do, and people can point you towards the relevant legislation and outline your options for responding. People have different individual preferences for their contact with the LA, but it's important to know that you have a choice.
You might enjoy meeting up with families in your area for a good chat and to see some examples of how home ed can work in practice.
Here are a couple of good websites to have a browse round. Both have sample deregistration letters as well as links to national and local forums:
Education Otherwise
Home Education UK
Hope that helps. Feel free to ask as many questions as you like!