When I'm trying to solo and switch from one scale to another I find it very difficult to choose the right connecting notes. Can anyone help to explain with theory or without how one finds these notes? Thanks

There are numerous ways to do this, each with an increasing level of difficulty. However, I would strongly suggest that you study the CAGED system to get you going. Learn how to form some of the arpeggio shapes, and the scale shapes that go with them. The idea being, that with caged, if you know which fret the chordshape should start on, you can then arpeggiate it as the music moves to it, and you should also know a scale position that works at that chordshape, to riff on. Then as the music moves to the next chord, you can find the fret to
make the new chord shape, and have a new scale to riff on. (You can even use the same chord shape and scale position to begin with, so all the fingerings are the same)

The overall learning effect is not much more difficult than learning where your barre chords are for each key, but it opens up the possibilities of using new sets of notes for each chord as it appears in the solo.

Hope it helps