Answer: That's a tough one. Do you mean visually, or aurally (by ear)?
Visually is pretty easy given the way the staff system works: from any line or space to the next adjoining line or space is always going to be some kind of "second" - two note names. Each line or space stands for a change in note name: A, B, C, D, E, F, G. From any line to the next line, or from any space to the next space, is always a third of some flavor - covering three note names. And so on.
Then to get the quality of the interval (major, minor, perfect, augmented, diminished) you have to be aware of how many half steps are included, and that's a little harder. It helps to learn to recognize the quality of the natural intervals in each clef, and then adjust if one of the notes is sharped or flatted.
Aural recognition is more difficult. Some people like to use familiar tunes as guides, for example the first two notes of "My Bonnie Lies Over the Ocean" form a major sixth. I don't think that is ideal, because the context in which you hear the interval might not match that of the song. The song might begin on the tonic, for example, while the interval you're hearing does not. I think it's better to learn the sound of a major triad and relate everything to that. That major sixth at the beginning of "My Bonnie" then sounds like two of the notes in the major chord, for instance, G - E in the chord C-E-G, if you're singing the chord with G in the low position: G-C-E. Fill in the missing C in your head. And that means this is a major sixth because the triad you're comparing it with is a major triad.
If you imagine a minor triad that would relate well to a minor sixth (G,-Eb, heard as G-C-Eb). A perfect fifth is the outer notes of the triad in its original position (C-G), a perfect fourth is the same notes if you sing the G below the C (G-C). Sounds complicated, but it quickly becomes instinct. Once you hear the primary intervals of the major and minor triads (fifth, fourth, major and minor thirds, major and minor sixths, octave) then other intervals are recognizable by how they compare to the ones you know: an augmented fourth is *almost* a perfect fifth, a minor seventh is *almost* a major sixth, a major seventh is *almost* an octave, and so on.
In Practica Musica the "Course 1" activity set has two activities particularly good for starting intervals: 1.06 Interval Names and 1.07 Interval Qualities. These activities include some on-screen explanation and help. And for further study you can use the Visual Intervals or Custom Visual Intervals activities to practice identifying intervals by sight (see Activities by Topic: Interval Names). For identifying them by ear you can also try Interval Ear Training or Custom Interval Ear Training or Speed Intervals, (Activities by Topic: Interval Ear Training) and there are some others that deal with recognizing several intervals at once, etc. There's a good one in the AP Course section that displays several harmonic intervals, plays one, and asks you which one you heard. But those Course 1 activities are the place to start. Note that the Course 1 set of 10 activities are done in order, so you need to start with the first and keep going until you reach 1.06., unless you've already completed the first 5. Course 1 is currently the only set of activities that works that way.
