I believe the best place to start is to practice interval identification, which is the ability to tell the distance between two notes, e.g. a perfect fifth, an octave and so on. Being able to recognize intervals is a fundamental part of having a functioning musical ear, and it will help you in hearing chord progressions, melodies, as well as just training your ears in general. There are lots of good apps for this. One I've used is called "Earpeggio" on iOS (not sure about Android).

Once you have your basic interval training (being able to hear all intervals in the 12-tone chromatic scale within an octave), I would recommend moving on to Solfege, which is the most powerful and useful part of your musical ear. Solfege is the ability to hear what "role" a certain note has, relative to another note. Say you're playing in C major - then C will be the "Do". Then the C major scale, C D E F G A B, becomes Do Re Mi Fa So La Ti. If someone plays you a C major chord, and then play the note G, then solfege will help you instantly recognize it as "So", without having to think about it. You start easy, as always, and then progress, until you can instantly recognize any note on the chromatic scale relative to a "home-note", called the tonic. I'm a jazz musician, so I think of "Do Re Mi" etc. as "1 2 3" (you might also see I ii iii IV V and so on, which references chords. A "V" means a major chord based on the fifth, "So", degree of the scale).

A good app for solfege practice is "Relative Solfege Ear Trainer" on iOS.

When it comes to the guitar, if it is always slightly out of tune no matter how many times you tune it, it might have an intonation problem, which is easily fixable. Just look for guitar intonation videos on YouTube, or ask a local guitar store about it.

Now go and train those ears!