What is it called when you cut 2 grooves in plywood so that they will interlock with each other perpendicular? What is the best tool for the job? Just a circular saw? A router?
A dado stack will be more versatile if you have multiple widths of plywood that you want to work with:
A straight router bit isn't adjustable in width, but it will produce a cleaner bottomed cut. They're often available in sets for different sizes of plywood:
If you'd rather not spend the money on either of those, you can always use a table saw with a regular 1/8" kerf blade and make several passes. Then you can clean up the bottom of the groove with a chisel. I wouldn't recommend trying this with a circular saw, but if you do, you'll definitely need to make a straight cutting jig for it.
You can join these pieces together like you ask, using a router, or table saw, cutting a narrow groove in either piece to join them together with a spline. A spline is a narrow piece of wood that is cut in thickness to fit the width of the saw kerf and ripped wide enough to fit ever-so-slightly less than the depth of both grooves when the pieces are assembled in their finished state. Glue is used on all joining surfaces to keep the joint together.
The tongue and groove joint mentioned by getterdun will work even better than a spline joint, the plies of the plywood is stronger than the solid wood of the spline method, although plywood can be used for the spline too.
I think the biggest problem is handling the material over the saw table, keeping it steady to get accurate cuts. The cut on the large face of the plywood will be easy, the cut on the edge of the other piece will be the problem for the spline cut, and this is where a router would excel. I would choose to cut a tongue on this piece, since the saw blade can be set so you cannot cut too much, an you can do repeated cuts to gradually get the tongue the right size to fit the groove of the other piece. Ideally your plywood will have no large bow to it or it will really make it difficult to get a good, consistent cut.
Another way to join these 2 pieces together is by using a biscuit joiner. This way the only thing you need to move around is the joiner itself, how the plywood lays is of no matter as long as the edge and face you need to cut is accessible and stable.
There is still yet another way to do what you ask, using a router would do pretty good here, or a stacked dado like Doresoom mentioned. I usually buy a small quantity of 7 1/4" circular saw blades and gang them together as I need to get the width of cut I need, using cardboard or paper with holes to shim the blades to fine tune the width of cut. (Careful of your saw tooth orientation if you use this method), in your case if you are using 3/4" material, you can get 6 or 7 really cheap circular saw blades and gang them up. Make your 1/4" deep cut in the one wide face and set the whole edge of the other to join the 2 together.
I understand that you want to connect two pieces of plywood perpendicularly, or at 90°. But I don't get the 2 grooves. I think you mean one groove and one tongue, hence the name "tongue and groove". I'd use a router. And to ensure a good fit I'd use a guide for the router and make sure that it's clamped "spot on" square to the work.