For harmony, study chord patterns out of first position : to best memorize, and know what you're doing (in order to reuse them by yourself) learn the patterns by noticing the relative postiion of the fundamental note (the one that give the name of the chord), and particularly the root fundamental on the pattern, the one that will be on the lowest string. Basically, these root notes are on 6th, 5th and 4th strings. If you work this way, you'll be able to play triads (packs of 3 notes) which are the core of chords in a way, but also the link to scales and melody, which are the key to improvisation and play what you want all over the fretboard.
For melody, study scales and all positions for each one. Start by basic scales such as major diatonic, natural minor diatonic, and minor pentatonic. There can be 2, 3 or 4 patterns for a given scale, and you can also combine them to cover the whole fingerboard. Some scale patterns are designed vertically, to stay in one position on the fretboard, and others are spread horizontally to cover all the fretboard. Working different patterns will make you play more out of the first position, and on all strings. Once you get a little bit used to it, you'll then make a link with notes, chords and triads, in order to play all over the neck with logic, and with a rich harmonic and melodic play.
It will require a lot of practice, but if you don't go fast, you'll get step-by-step results quickly. You don't need to read music, learn theory, or harmony laws first, even if it helps alot to go further. First, train your fingers and your ear : throughout your pratcice, listen to what you're doing and you'll improve.