Hi Tzoaie and welcome to the forum.
The harmonization varies from piece to piece really, but usually involves at least some element of improvisation. For most of the pieces on my Piano Sketches album, I initially tried inverting the underlying chord sequence and modifying the voicing until it sounded right on the piano (e.g. the intro to Us Prisoners and the minor-key theme that appears half way in Egyptian Concerto, Part 1). For the pieces on my second Reflections album, generally I've been only inverting Beatles melodies from various parts of their songs and then creating brand new harmonies around that (mainly by improvisation) to fit with the rest of the piece.
Also note that if you invert a complete portion of music then it will also automatically invert the harmonies. For example, if you find a section of music where the left hand is playing a chord and the right hand is playing a melody, then inverting it will generate an inverted version of the chord played in the right hand and inverted melody in the left hand. A good example of this is a section of my piece Egyptian Concerto, Part 2
(from 7:04 until 7:14, which corresponds to bars 148-152 of the sheet music). This is an almost exact inversion of the start of the second movement of Rachmaninoff's Piano Concerto No 2.
Harmonization in general is an area where there is a lot of room for experimentation and personal expression; chord voicing in particular is very personal and a core part of a composer's style, and I'm trying to develop my own particular style of chord voicing as I go on to create a unique sound.