I was taught to make Krenov style handplanes by David Finck, a man whose work I so admire, he could tell me that chocolate-covered dog poo makes a superb finish and I'd believe him.
David wrote the book "Making & Mastering Wood Planes" (pricey because it's out of print, but if you write David, he will let the publisher know they are in demand). His book is not only a recipe for making planes, it covers: tuning your bandsaw and several handtools; sharpening techniques; making a grinding jig, a routing jig, a small hammer, & a sharpening stone cradle; planing techniques & planing jigs; and more.
The body of the Krenov style planes consists of two side pieces, a front piece, and a back piece. Because they are laminated, it makes construction easier than planes constructed with a solid chunk of wood. Two other pieces, a wedge and a pin, which holds the wedge and iron in place, complete the plane.
David sells plane irons on his site that take a long time to sharpen but which hold an edge for a very long time.
The most difficult part in making these planes, at least for me, is opening the throat. You must be patient, because it's easy to remove too much wood and create too wide an opening for shavings. Two benefits of a thin opening are less chance of tearout and a smoother finish. However, your iron must be extremely sharp, otherwise the shavings will jam up.
The second most difficult part is fitting the wedge. It must contact the pin, ideally along the entire width of the wedge, but at least must contact the outer edges of the wedge. This ensures your iron will be held firmly in place.
David wrote an article in Fine Woodworking issue #196 that gives you an overview of building a plane. So if you aren't able to find David's book, you can at least read his article.
One more thing...David recommends oil, shellac, or nothing as a finish for the planes. Not dog poo.