When is distance reduced to 0?

When two objects gets closer to each other, you can measure the distance between the two of them, and see how that value gets smaller and smaller and smaller. Soon you'd be working in decimals such as 0.8mm, 0.1mm, 0.000000001mm etc, but obviously using...

smaller measurement terms. Now my question is, how much can we reduce that distance by, before we can say they are now touching, and the distance between the two objects is 0? What's the value that comes just before it reaches 0?

Actually, there is no limit to how close an object can be to another. Technically an object could be 0.0000000000000000000000000000000000000001μm from another object, but that still means the distance between the two can be made smaller. There are infinite decimal numbers between 0 and 1 and so I think that should just about answer your question, lol.

I would think for an object to truly be touching another object, it would have to form together. (ex. two drops of water running together)

yeah, if you want to get super technical about it, they will never touch unless they bond, but besides that, they're eletrical charges will not allow them to touch.