NeoPixels are very easy to connect requiring just three connections:

• GND - ground
• Positive supply 3V (in the case of the micro:bit)
• Data Input - data is streamed into the chain of NeoPixels, each NeoPixel passing on the data to the next one along the chain. When the data stops all the NeoPixels show the color that their data indicates. Connect the Data Input connection on the NeoPixel display  to Pin 2 of the micro:bit.

In terms of electrically connecting to the display, if you are using the suggested 24 pixel ring then you can use alligator to male header pin leads to connect up the display by pushing the male header pins into the pins marked GND, PWR and Data In.

Poking the pins through the holes like this is fine for trying things out, but to make things more permanent, solder the pins from the top side of the board and clip off the excess pin.