Interval Ear Training
An interval is the distance between two notes. A good way to begin training your ear is to learn to recognize different intervals going up and down. Being able to sing (or think) intervals is equally beneficial. An easy way to do this is to associate each interval (ascending and descending) with the first two notes of a song. It's important to choose a song that you're very familiar with, often kids songs or christmas carols work the best because they are deeply engrained into our minds. Here's a list from wikipedia of possibilities but feel free to come up with your own.
Some intervals are easy like seconds, fifths, fourths. Others are pretty tough like thirds, tritones, and sixths.
Here is a good exercise- start by recording yourself playing the note 'C' and then playing 2 notes at random (hopefully the 2 notes at the same time if possible) and repeating it with a number of different combinations of notes. It helps to play a 'C' in between each pair. Then take a break and go back and listen to the recording while figuring out what the 2 notes are by referring to the 'C'. This very beneficial for your ear and once you're comfortable with it, start playing 3 notes and then 4 notes etc.
I can't emphasize enough that this type of work is HARD but after a grueling session I promise you will be able to hear and enjoy music like never before.