What's the best way for inexperienced cook to finely cut cabbage?
You can try using a good long sharp knife and a large wooden cutting board like Michael mentioned but it can be slow if you're inexperienced. Other cutting boards will dull your knife quickly which is why I mentioned a wooden one.  

The only other way I know is to use a mandoline. You'd have to first cut the cabbage small enough to use but I know for myself, it would be a lot faster than using a knife. (And I'm an experienced cook too!)

If you do much food preparation and cooking, a mandoline is very useful to have. I'm not sure if you'd consider $50 (rough estimate as I don't know where you live) expensive. The best, in my opinion, for a home cook is a Börner mandoline. It's German made and does a great job! I'm not advertising their product - only stating that I think it's one of the best. You can check this video that compares a number of different reasonably priced mandolines. 
https://youtu.be/I15-htHJF_I