There are a lot of threads on sharpening and de-rustifying, so I'm not going to comment on those. The 78 is a good plane, but yours is missing the fence and the depth stop. I can't tell from the photos, but you may also be missing the nicker that lets it work easily across the grain.
Without those, especially the fence, that plane is... well, not useless, but a lot harder to use. It will still work fine for cleaning up tenons and things like that, but using it to actually cut rabbets is going to be a challenge. If you want to try anyway, here's my advice:
1) Clean and sharpen it, and make sure the sole is exactly perpendicular to at least one of the sides.
2) Mark the width and depth of the rabbet with a knife, and, especially if you're going cross grain, score it as deeply as you reasonably can.
3) Start cutting with the plane tipped sideways, so one corner is in the score line. Make a few passes that way.
4) Once a good trough is established (2 or 3 passes in pine, a few more in hardwood), start tilting the plane back to level, letting the trough guide the edge.
5) Once the plane is flat, make sure the shoulder you've established is perpendicular to the surface of the wood (you may need clean it up with the plane tipped on its side), plane down to the depth you marked.
I've done this with an old skewed rabbet plane that had no fence, and it worked fine. It takes some practice, though, so start out working on a piece of wood that doesn't matter.