Steps:
1. Mark out your pattern on first side of cabinet.
2. Cut the straight segments using a circular saw with a straight edge guide (best) or a jigsaw.
3. Use the jigsaw to complete the curved or radius areas.
4. Sand the edges until you are happy and things are smooth.
5. Use the first side to mark out the second side as a template.
6. Cut out the second side staying slightly outside the lines (jigsaw is fine here).
7. Attach the two sides together using clamps or screws. Use a "pattern flush trim bit" with a router the flush the second side to the first side and make them identical. A flush trim bit is just a straight or spiral router bit with a bearing that is exactly the same diameter as the cutter, allowing you to use another piece as a template.
8. Separate the two sides and move on to the rest of the cabinet. Rinse and repeat for duplicate parts.
Rick