Here are a few contemporary photographers known for their work with light painting:

LAPP-PRO. The person behind LAPP-PRO is JanLeonardo and he’s one of the best known light painting photographers right now. His work combines choreographed manipulation of light, performance art, time, and photography.
Hannu Huhtamo. Hannu Huhtamo is known for his flowers and structures that look as though they could be CGI creations.
Michael Bosanko. Michael Bosanko’s work has a playful, whimsical quality. He uses light to create otherworldly scenes that can include humans, animals, and well-known motifs.

To get started you will need:

A camera with manual or bulb exposure control - to achieve the long shutter speeds necessary.
A sturdy tripod or sit your camera on a sturdy surface - the exposure will be measured in seconds so handholding is ruled out
A light source - this can be a wireless flash, torch, led tubes, anything that emits a bright light, the more variations in size and colour the better
Other useful items - a cable release, extra batteries
A dark place or scene - can be indoors or out

How to setup:

Decide on your shoot location and place your camera on the tripod or a sturdy surface
Switch your camera to manual mode and set your ISO to 100, a small aperture, such as f/11 or higher f number and shutter speed to between 10-30 seconds
Fix your white balance depending on your light source, try “incandescent” or “tungsten”
Your camera won’t focus in the dark so pre-focus on the area you wish to shoot, switching your lens to manual focus
If using a shutter release attach that now, alternatively use the 2 or 10 second timer to prevent camera shake when pressing the shutter