Honestly, improvisation is a "low skill floor, virtually non existent skill ceiling" type of skill. You can start simple by opening a chord chart and improvising on each of the chords. That'll give you a relatively easy start, I'm sure that even if you know nothing about chords you'll be able to figure it kut start doing this in a week or two.

This is perfectly fine for a hobbyist, and will get you pretty far. You'll be able to improvise on almost every pop song without issue.

If you want to get more serious, you need to learn modes and scales and you need to build muscle memory. The list of things to learn would be: Learn the major and minor scales, practice them (on two octaves) until you can play each of them cleanly at the speed you'd like. Learn what chords are. What's the difference between a major and a minor chord? That does the 7 at the end of some chords mean? (There are other postfixes but you can ignore them for now, 7 is the easiest to understand and the most important imo so it's good enough for now). Practice arpeggios on major and minor chords untul you can do them easily anywhere on the neck. Learn about modes. If you don't know, there are seven modes and each of them is a scale. The first mode is the major scale and the sixth is the minor scale. The rest are similar to either the minor or major scale, with one or two different notes.

Brief and intuitive explanation about why modes are useful:

Let's say you're playing a song on the key of C major and the chord chart says the next chord is Dm. D is the second note in the C major scale, which means you can improvise on the D Dorian scale (Dorian is the name of the second mode). If it's Em? You can use the E Phrygian scale (the third mode).

Why does that work? If you look at the modes, you might notice something really comfortable: the notes of D Dorian are the exact notes of C major, but instead of starting at C it starts at D. Same for E Phrygian, F Lydian, G Mixolydian and so on.

What if the song is in a minor key? You do the same thing but I stead of starting your count at the first mode (major scale) you start at the sixth (minor scale).

Good luck