How to Clean wood furniture - or partially refinish..can anyone help me?

Does anyone have any experience in "renovating" furntiure? I have this dining room table set - about 28 years old. Solid real wood. Table top is perfect and can't have anything "done" to it as it is specially treated for a hard shine kind of thing. The legs and the chairs are the problem. I can have the seats re-upholstered, no problem. But the wood look dirty. It is a medium brown color and then stained a little darker. It has engraved leaf designs up the backs of the chairs. It looks like it has black stuff ... dirt... on many parts and the "shine" is long gone. It has been in storage for the last 6 years.

I want to see if I can clean it and make the wood look nice and clean, maybe do another stain and then a clear coat. No sanding or anything expensive. I have no experience of any kind with this kind of thing. I'm a "needle in the hand" craft person!

Anyone have any suggestions or experience as to how I can at least give it a try to see if I can make it usable again? Are there any cleaners that would remove the "dirt" or whatever it is. I always dusteda nd polished it - but I have another little 2 -chair set of a lighter wookd and that same black stuff is on it. I took a sponge and warm soapy water and scrubbed at and it took off what little shine there was and even some of the wood color (possibly the stain?) and almost like I sanded it, but only used a kitchen sponge with a light touch of the scrubber on te back - I know I couldn't do it hard or what happened would happen, but it happened even tho I didn't use it very hard. So that is my experence!

Anyone have any helps for me? Thanks so much!