Open the image in Photoshop
Duplicate the background layer
Increase contrast using Levels or Curves
Convert the image to black and white if needed
Clean up the image with the Brush or Eraser tool
Use the Pen Tool to trace the main shapes
Create vector paths for each section
Convert paths to shape layers
Fill shape layers with solid colors
Save the file as PSD to preserve layers
Export the final vector artwork as SVG, PDF, or EPS if needed