Everything you want to do is at least technically possible by hand: people have been making tables for a long time, and power tools have only really been around for a couple hundred years. I made a pair of frame-and-panel toy chests using nothing but hand tools (well, and pre-dimensioned lumber, which counts for a lot), which is a much more complex project.
Basically, there'll be 4 legs and a top...haha. It'll be pretty simple. I'm at work overseas, so I can't upload any plans, really. The legs will be 4x4 posts, the top will be from 2x6's (or 2x8's, can't remember). The apron will be from the same 2x's. It is hardwood, from a pecan tree that fell over on my property.
Ok, here we're starting to get some useful information!
The sliding dovetail has crossed my mind. I may use that, but I am looking for something I can do without use a power tool. And, yes, I am certain I want to do it. Why do you ask?
As far as joining the 2x's together, I'm not sure about that yet, either. I have thought about t&g, but I am open for suggestions. I'm not in a hurry. We're having a new house built, so it would just be sitting in the barn for a while if I did it now.
Sliding dovetails can be cut by hand. I haven't tried it yet, but that's more lack of interest than anything else. In theory, it's pretty simple: cut the socket sides using a saw, then chisel out the waste; cut the dovetail piece with a saw and chisels; drive them together with a mallet. Simple isn't the same as easy, though. :grin:
Anyway, here's my advice. I'm picturing something like this, so all my advice is based on that.
1) Use glue. Yes, you could do all of this without glue, but it's not worth the effort. Nails have been in use since Roman times at least, and screws since at least the 1700s. Hide glue has been available substantially longer than those, and these days you can buy it in a bottle that doesn't require cooking your own.
2) For the top: Your best bet is to joint the edges of the boards, then glue them together. Glue joints are typically stronger than the surrounding wood, so that's all you need to hold it together. If you really insist on no glue, you could do something like a pegged breadboard end, but I can assure you it will break sooner or later. I've made the mistake of making a long-grain connection like that, and it didn't last long. I suppose you could also do a pegged frame and make the inner surface out of boards floating in grooves, like a giant frame and panel door, but I suspect you'd come to regret the gaps in it pretty quickly.
3) Fastening the legs to the top: Traditionally, you'd probably put a skirt around the table, fastened in some way that wouldn't prevent wood movement in the top, and fasten the legs to that. If you insist on not using screws or nails, you could fasten the apron to the legs with sliding dovetails, then put pegs in the top of the leg for the table top to sit on. A tabletop 2" thick will weight quite a lot, so gravity would probably hold it in place just fine. You could also do a joint like this to hold the apron to the legs:
It's more work, but probably easier to do. The two aprons interlock, and sit in a cross-shaped mortise in the top of the leg. The peg would probably best go in the inner corner, I think... that feels like it would probably provide the best durability.