That's got some obvious mission-style elements but it's not a purist's interpretation, and I doubt there's a traditional or "correct" way of building it. Do you have a better picture that makes the construction of the top clearer? It seems pretty unlikely that it would be one massive, solid slab, so my guess is that it's plywood framed with a tall, solid edge, in which case those edges might act as stretchers.

Thanks for the comments jon. Unfortunately I don't have any other photos - I found this one online while surfing for inspiration.

Those legs look to be about 6x6. Assuming that you will make the top of plywood with a framed edge, I would screw a top plate of plywood about 16" x the width of the top to the top of the legs and then screw that top plate to the bottom of the top. That, combined with the bottom stretcher, should make it quite sturdy.

Thanks for the suggestions guys. I want to do the top as a solid slab so I can have a hand-planed/scraped look to it, probably with exposed end-grain on the ends to show it's solid and for a slightly rustic look.

I'm thinking I might use trestle-style construction for the top of the legs and for the attachment. That is, connect each pair of legs on each side with a stretcher across the top of the legs. Then drill some enlarged holes and use screws with washers to attach through that to the top. And also beef up that lower stretcher for strength.

That looks like a lot of Frank Lloyd Wright furniture. There are many books on his furniture that probably have some good details about the consrtruction. You could take a look. It might haelp.