Running a Relay on DC
Firstly, think about what you're doing here. You say you're an electronics noob and you're playing with mains electricity.

You've kind of got the idea of the circuit, but missed out the optocouplers and various power supply inputs that are present on your relay board. My suggestion would be to do this in a safer way to start with, using say, a 12v battery and a 12v lamp or an LED instead of jumping straight into working with the mains which, could kill you, burn down your house or blow up your laptop if you get something wrong.

So, how to make this work...

Replace the 250V supply with something low voltage and safe, say 8AA alkaline batteries in a holder or a PP3 battery. Replace your 250v LED with a low voltage lamp 12v, 9v, 6v or whatever is close to your supply voltage, or ideally, an LED with a suitable series resistor (1k or more should do for a maximum of 12v) to limit the current.

The relay board has optocouplers, these need to be powered on the low voltage side via the Vcc pin. There's another Vcc pin on the relay board probably for the 5v relay coils. You'll also need to connect all the power supply (GND) ground connections on the input side together otherwise it won't work.

The 5v relay coils probably won't work from your 3.3v powered Node MCU but the optocouplers may.

Once you get the whole thing working with an LED, you can progress to wiring it for mains operation, but learn some more about mains electricity safety before you do that.

You shouldn't be messing with your bits and pieces of circuits on a breadboard. You'll have a proper enclosure which can be closed up to prevent you getting a shock or an eyeful of molten metal if something goes wrong. You'll also have properly fused the supply, be running it through an RCD and will have earthed the box if it's metal.