In order to have a practical microscope or diffractometer, just having an electron beam was not enough, it needed to be controlled. Many developments laid the groundwork of electron optics; see the paper by Chester J. Calbick for an overview of the early work. One significant step was the work of Heinrich Hertz in 1883 who made a cathode-ray tube with electrostatic and magnetic deflection, demonstrating manipulation of the direction of an electron beam. Others were focusing of electrons by an axial magnetic field by Emil Wiechert in 1899, improved oxide-coated cathodes which produced more electrons by Arthur Wehnelt in 1905 and the development of the electromagnetic lens in 1926 by Hans Busch.
Building an electron microscope involves combining these elements, similar to an optical microscope but with magnetic or electrostatic lenses instead of glass ones. To this day the issue of who invented the transmission electron microscope is controversial, as discussed by Thomas Mulvey and more recently by Yaping Tao. Extensive additional information can be found in the articles by Martin Freundlich, Reinhold Rüdenberg and Mulvey.
One effort was university based. In 1928, at the Technical University of Berlin,  (Professor of High Voltage Technology and Electrical Installations) appointed Max Knoll to lead a team of researchers to advance research on electron beams and cathode-ray oscilloscopes. The team consisted of several PhD students including Ernst Ruska. In 1931, Max Knoll and Ernst Ruska successfully generated magnified images of mesh grids placed over an anode aperture. The device, a replicate of which is shown in Figure 5, used two  magnetic lenses to achieve higher magnifications, the first electron microscope. (Max Knoll died in 1969, so did not receive a share of the Nobel Prize in Physics in 1986.)
Apparently independent of this effort was work at Siemens-Schuckert by Reinhold Rudenberg. According to patent law (U.S. Patent No. 2058914 and 2070318, both filed in 1932), he is the inventor of the electron microscope, but it is not clear when he had a working instrument. He stated in a very brief article in 1932 that Siemens had been working on this for some years before the patents were filed in 1932, so his effort was parallel to the university effort. He died in 1961, so similar to Max Knoll, was not eligible for a share of the Nobel Prize.
These instruments could produce magnified images, but were not particularly useful for electron diffraction; indeed, the wave nature of electrons was not exploited during the development. Key for electron diffraction in microscopes was the advance in 1936 where  showed that they could be used as micro-diffraction cameras with an aperture—the birth of selected area electron diffraction.
Less controversial was the development of LEED—the early experiments of Davisson and Germer used this approach. As early as 1929 Germer investigated gas adsorption, and in 1932 Harrison E. Farnsworth probed single crystals of copper and silver. However, the vacuum systems available at that time were not good enough to properly control the surfaces, and it took almost forty years before these became available. Similarly, it was not until about 1965 that Peter B. Sewell and M. Cohen demonstrated the power of RHEED in a system with a very well controlled vacuum.