Lasercutting
Design
Design the image in the CAD software of your choice. Export to .svg or .dxf. You'll need to adjust your design because the laser removes a kerf.
Cutting
Check with the shop you're using on whether they can cut the material you want. Cardboard and wood are usually fine, but plastics vary widely in gases released. Be sure to turn on the ventilation before you start cutting, and wait a few minutes after the cut finishes with ventilation running to avoid letting out gases. Be sure to properly focus the laser to the material's height.
Engraving vs Cutting
Raster vs Vector