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

Mandolines can work, but there's a problem -- cabbages are round, so the leaves aren't flat. This makes it more difficult to cut everything in only one plane, such as would happen with a mandoline or shreading disk on a food processor.

Although people have said 'use a long sharp knife' and similar, they haven't mentioned the technique:

1. Remove any outer, discolored leaves
2. Cut the cabbage in half, through the axis of the stem/core. (likely the most difficult step; a really long knife helps)
3. Cut each half into quarters, again through the axis.
4. Cut the core out of the quarter, by taking a diagonal slice. You want to get the core out, but don't cut so far that you're removing the firmly backed bit around the core.
5. Place the diagonal slice against your cutting board.
6. Slice to the desired thickness.

I start cutting the top / thinner parts of the leaves first, angling slightly so I'm not getting sheets at the top, and work until I'm into where the core was. I might continue the whole way down from that end, or reverse it at some point (as it's easier to get really thin slices from the bottom while there's still something to grab onto; you want thinner slices where the leaves are thicker)

For really huge heads, I might work on eights, not quarters ... or start with quarters 'til I'm to the core, then split it again to finish the slicing.

You might be best off buying a mandolin, however usually they aren't wide enough to fit a head of cabbage.

To make it easier, try slicing the whole head of cabbage in half, so that you have a flat surface to slice the cabbage.

P.s. it's good practice!!

i use a 14" mezzaluna knife to cut cabbage to the size you're describing. The one i have was $10 on Amazon. It's not currently available, but i'm including a link so you can see what it looks like: https://smile.amazon.com/gp/product/B00PV3WJHI/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1

There are videos on YouTube showing how to use them. It's pretty easy, but it takes a couple minutes to get used to the unusual shape. This type of knife is also known as a hachoir. Here are some YouTube videos: https://www.youtube.com/results?search_query=how+to+use+a+mezzaluna+knife

Before thinking of other tools because you assume you cannot do it with a knife - check that the knives you have are up to scratch (sharp, and not having a geometry that will make the task hard). If yours cannot cut off a slice with either one backward or forward stroke, or at most one forward-backward cycle... or if the balance means it is hard for you to control it... it is the knife that is ill suited to the task and not you.

Ask someone experienced to observe how you handle a knife and to point out some corrections. Basic knife skills can be learned in half an hour or less - the rest is practice. There are many inefficient habits to using a knife, and it's very, very useful to get rid of them. A cook once showed me how to slice stuff safely and efficiently, and now I do most things with a knife for which I previously would have used some special tool (garlic press, mandolina, herb grater).

Common mistakes include using a dull blade, a too small surface to cut on, and pushing the blade towards the surface (slow chipping) rather than using a forward/backward motion (sawing). Use the knuckles of your left hand (if you're? a righty) to guide the blade, by holding your fingers in a crimp. By only slightly adjusting the angle of these supporting fingers, you can cut very fine slices. Always having your finger pointing downwards and your thumb locked prevents injury. For a large object like a cabbage, or a small layered and slippery object (onions), you need to cut it in half or quarters and place the plane surface face-down.

However, this is all really awkward to explain in writing and not so easy to pick up in reading it. As I said in the beginning: have someone show you how to efficiently handle a knife. It is more simple than you think and will make your life so much easier!