How to connect different wire colors
Can’t do it
The unusual wire colors mean one thing: this house has conduit for its wiring. That would only happen if your jurisdiction requires it.
It’s rather unfortunate.  If you had spent hours watching Youtube videos on extending circuits with metal conduit, you’d be eager to get into what happens next.  Sadly you watched videos on extending circuits with “Romex” (NM-B cable), so you have a strongly held expectation that you’ll be doing that next.
You can’t.  It’s illegal.  At the time you’re selling your house, the inspector will flag it, and you’ll have to pull a permit to tear it out, tear it out, pull another permit to put it back in, then put it back in right.
You’ll need to run up to the lamp location with conduit, using proper conduit laying methods.  At that point you can get some THHN wire, a white wire for neutral and red for switched-hot, from the switch to the lamp inside the conduit.
The wires.
Neutral is the white one, and probably does not go to the switch.  A voltage tester will show one is always-hot; that goes to the switch.  The other one will be hot when the switch is on; that one goes to the switch and lamp.