You can associate an interval with two notes of a popular song already well ingrained in your memory. For instance, you might remember the minor third interval as the first two notes of Black Sabbath's "Iron Man," the augmented fourth as the first two notes of West Side Story's "Maria," and the minor seventh as the first two notes from the original "Star Trek" TV show theme. Practice intervals with these song associations in mind until translating the sound of an interval into the interval name becomes second nature.
Find a friend who is a skilled musician and ask him or her to help you with interval training. Start by having your friend play only simple intervals that are easy for most people to hear, like the octave, major third, and perfect fifth. Practice with the notes played both separately and at the same time and in a wide range of keys. As you get better, integrate more intervals like the minor third, major sixth, seventh, second and perfect fourth. Finally, add the remaining intervals to your repertoire until you've mastered them all.
Find a free ear training quiz online that will automatically test you on intervals. Many sites offer ear training with both chords and individual notes played at intervals so that you can become facile with both. You can also take an online quiz to test yourself and track your improvement at identifying intervals. Practice with several different voicings, keys and octaves in order to master the full range of possible chords and intervals. You'll not only improve your musicianship as both a composer and performer, you'll also add to your own personal appreciation for music.
Practice reproducing musical intervals by first picking an interval, then singing or playing that interval on your instrument. Check each interval as you go, whether with another instrument, with a musician friend or using an interval training computer program. Practice intervals going up and going down the scale and in every musical key. Increase your practice speed until you're able to reproduce an interval as quickly as you can hear it in your head or say its name.