Refinishing help please  

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Just my opinion, but is extremely important to show the entire
table to give good restore advice. Yes, it is oak. Are you sure it
is Danish?
A table surface is often very dry and stained over time from being
used for drinks and cleaned often. The key hint to a restore is the
underneath and other surfaces. They often need to be treated a
bit different.
Dozens of very good step-by-step restore advice if you google
'restoring old oak'.

Thanks Rockland..
...that's great. It's definitely Danish, there's a stamp on the back.
I have done some research, but when I do look in to refinishing there's usually sections on scratches, stains and discolouring but nothing for all these combined. I'm just fearful of messing it up.
Dan

Not so sure it's oak.
Looks more like walnut to me. Perhaps with a worn out oil finish. I don't see anything that would indicate a failed varnish.
The scratches and water stains are not such a big deal, but the ring may be problematic. If the ring is an oil stain, it's possible that a light sanding and reapplication of an oil finish will even the color out. If the ring is caused by a reaction like that between natural tannins and iron, it would need to be bleached, but that can be tricky.
I'd give the whole piece a good rubbing with an old linen dish towel and mineral spirits or naptha first, being careful not to snag any rough spots, loose veneer, or burn down your house. A test spot with some denatured alcohol on a Q-tip will tell you if anything else is likely to come off. It's entirely possible that the table simply needs a good cleaning, a light sanding, and a fresh application or two or three of oil followed by paste wax.

I agree
Unless it's really messed up, the best thing to do is to give the wood a good drink and polish and live with its original condition, whenever possible.

I....
...bit the bullet and gave it a light sanding. It was the one thing I didn't want to do, but it's come out really well and after applying beeswax, it looks great. I think I was over-worrying!

Never on time!
Bit late but for the next time try fine wire wool instead of sanding. Use beeswax and rub the same way you would with sandpaper. Gives iy a great finish without the damage that sanding can do.

Thanks Arthur
I did that on some of the surface but I couldn't get the stain out without sanding. I think I was lucky with wood type though as it sanded easily.

looks like teak to me..
looks like teak to me..

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Looking again i think you are correct. Teak or walnut. When a surface is
so dry, thirsty, even slightly weathered by being exposed to the elements,
it is hard to identify. The grain pattern is similar to my teak chair backs.
I was focused on the object, being handed one tiny
clue to what it is.

The great thing about "Danish oil" finishes
is that they are so easily repaired. The not-so-great thing about them is that they so frequently need it.

photo
can you show the whole piece, from what you're showing us it doesn't look like much and my be a waste of your time to refinish.

nearly done...
...i'll post a pic once I've finshed the transformation