An simple way to get started with recognizing intervals by ear is to consider the first note of an interval as the root of a major scale. Then listen to the second note decide what scale degree that second note would be; 1st, 2nd, 3rd, etc. If the second note is a 4rd or 5th then it's a perfect interval. If it's any other scale degree then it would be a major interval.
That covers major and perfect intervals. Once you have them under your belt the minor intervals should come easier since they are just a half step lowered versions of their major counterparts.