I am looking to build this table. The design is simple and I like the basic style. I do not have a Kreg Jig to drill pocket holes to attach the 2x4 rails to the legs. How else could I secure these without going through the outside of the leg? Its going to be outside for the summer and moved to a garage in the winter so they need to be as sturdy as possible.
The following is a fairly classic way to do this.
The 2 by 4s get glued and screwed to the table top with a diagonal cross piece at the corners.
The legs then get placed and screwed or bolted to the diagonal so it gets pulled tight.
If you use lag screws, or the like, the legs come off pretty easy for storage.
Trevor's idea is a good one, but you wouldn't need specialized tools to do a pocket arrangement. A Forstner bit would allow you to create suitable pockets in the inside face of the rails, and you can then simply bore in from the end.
In a pinch, a simple cheap spade bit would work, but you'd want to grind the guide point down to 1/4" or so.