Here is a typical section through a wall/floor junction in the UK, using either shallow strip or deep strip foundations.
Basically, we start by digging a foundation trench. Then we fill with unreinforced concrete to the desired depth (deep fill is more common nowadays than shallow strip). Then we build the base of our walls, usually up to damp proof course. The walls are used as formwork for pouring the ground bearing concrete floor or for supporting beam and block flooring. Only after that stage is complete do we start raising walls above dpc.
This is for the vast majority of foundations in good ground. In poor ground, we might use a raft foundation or, more usually, some kind of piling.