Generically, this is a 3-way switch light circuit with two motion sensors. Let's start with the 3-way switch light circuit. Based on comments, OP is totally new to electrical wiring. So I will start with a paraphrase of Harper's usual advice:
- Read, read, read. Get some books (you can borrow from the library in most places - no need to buy if you don't want to) and read up on how to do residential electric wiring. Watching videos and reading things online can help a lot too. The problem is that a lot of online information is of questionable quality. A published book generally sticks to code and proper practices.
- Practice, practice, practice. For example, when it comes to using wire nuts, practice on some pieces of wire and wire nuts before doing the real work on the permanent wires in your house.
And some terminology:
- Cable - In most places you can use non-metallic cable, a.k.a, "NM cable" or the trade name "Romex". In some places you must use individual wires inside conduit - if that is the case then there are some more steps involved. This type of cable is referred to as /2 if it has two insulated wires (black and white) plus bare ground. /3 has three insulated wires (black, red and white) plus bare ground.
- Box - also "switch box", "junction box", "receptacle box" - these are all the same, except for size. Often the same box can serve all sorts of functions depending on what is placed on the front of it. Boxes are available in both plastic and metal forms. I prefer metal for a whole bunch of reasons.
- Cables must be inside walls or if they are outside walls they must be protected from damage (e.g., covered with wood or Legrand Wiremold or placed in conduit).
The typical setup for a 3-way switched fixture (there are many variants that are actually equally OK) is:
- /2 from power (e.g., from an existing receptacle box) to switch box 1
- /3 from switch box 1 to switch box 2
- /2 from switch box 2 to light fixture
In some cases, the light fixture is a hard-wired device. In other cases it may actually be a receptacle with a power pack (transformer) plugged into it.
In a traditional 3-way circuit, the 3 wires vary in function but in the above configuration neutral + 2 travelers. Depending on the position of switch 1, one or the other traveler is hot at any time and the other wire is not hot. Then depending on the position of switch 2, either the hot or not hot wire is connected to the light fixture.
Now we get to the complications. Motion sensors are common add-ons to simple switches. But they need power to work. In a standard 3-way configuration, the 2nd 3-way switch does not have power available for its internal functions! That is a big problem if you need motion sensors in two places.
Smart switches to the rescue!
A smart switch is essentially a tiny computer hiding inside a switch. Depending on the type, it can include WiFi access, other remote forms of wireless control and/or monitoring, timer, dimming and many other things. One of the great things about smart switches is that they can use a number of different methods to communicate with each other instead of using two travelers. As a result, many (not all) smart switches can communicate using one wire for hot (always hot), one wire for neutral and one wire for signaling.
Now to see if we can find a smart switch to do what you want...
One possibility is Lutron Caseta. They have a motion sensor which can be added to a system of Caseta switches. Which means you should be able to use a Caseta switches at the top and bottom of the stairs and "link" them to the motion sensors.
I highly recommend having actual physical switches at the top and bottom of the stairs, even with motion sensors. There are times when motion sensors don't react as quickly as you would like, or turn off the light because you are sitting on the stairs for a few minutes, etc.
