They're Out There
If you listen closely to the vocal tracks on most pop songs, you'll find tons of harmonies. You'll not only hear them on the chorus but peppered throughout the rest of the track too. Most vocalists like to stick a harmony on a couple of lines throughout the song, not just the chorus. A lot of the time, it's layered in the background, just lifting the line without making it too obvious. Sometimes the vocal will be doubled, sometimes it's the lead an octave above or below, and of course the traditional 3rd above is always popular. Doubling and singing the same line an octave above or below is also vary effective in bringing something extra to the line without having a full blown harmony there. Some artists will almost always double their vocal line.
What people don't realize is that each style of music has it's own way of dealing with harmonies and vocals. Some styles (like metal) generally don't like 3 part harmonies unless it's for a special effect. Other genres (like country) use harmonies so much, that it's pretty much part of the style. Jazz of course has it's more complicated harmonies, but usually used more in vocal groups (versus the intimate trio setting). Certain types of rock and indie rock also use different harmonies to create different moods (Alice In Chains is a great example of unique harmonies being part of their style). RnB harmonies also can go beyond the typical intervals to great effect.
Some Of The Rules
Straight ahead harmonies follow simple rules that can be used as a starting point (as well as ending point) for some of your songs. Most harmonies will follow the chord or 'harmony' behind the vocal line. Depending on your melody, your harmony will usually be a third (or fourth) above (or below) that. For example if your chord is a C major and your vocal melody starts of an E note, goes up to an F, and returns to and E, your harmony line will be a third above that (i.e. G, to A, back to G). However, if your vocal melody line starts on a G, goes up to an A and back to a G, your harmony line will be a fourth above that (i.e a C, to a D, back to a C). It doesn't always work exactly this way because your melody doesn't always start on a convenient note, but it's a good starting point. Also, depending on the genre, different harmonies will apply. If you're singing harmony on a blues song, or a reggae song, different harmonies will apply. Still, a third is a great way to start.
Get It Going
The best way to get started in using harmonies is to just get started. Don't worry about too much of the technical stuff to begin with. Just try singing along with songs and try doing the harmonies. We'll go into some exercises that will help you along the way but it's best to just get going. A lot of vocalists I've worked with didn't work on harmonies as much because they were a mystery and had trouble at the beginning. Try working on these and see how far you get. The best harmony singers I've ever used had a great ear and would come up with the best harmonies. There are two ways to go about figuring out and working on harmonies; a) strictly technical (following the line exactly) and b) experimentation (not following the line). These both occur in music for different reasons. Most of the time when singers are in 3 (or more) part harmony, you have to be a bit more strict about the lines because you don't want the different harmony lines tripping over each other. The second happens a lot with just one line of harmony where the harmony line won't follow the melody line exactly. Examples of this is where the melody will move but the harmony will stay on one note (or move around very little).
Start by playing a chord on the piano. Keep it simple to start. With your right hand play a simple melody. Start with using chord tones only. The example listed above is a great example to start with. Play a C chord. Play the melody above that: C to D back to C. Now you're going to sing the harmony. Play the E to F just above the C to D you just played. Hear those notes in your head. Sing them and try to remember them. Now play the chord with your left hand, the melody notes C and D with your right hand and sing the harmony notes E and F all at the same time. It's important when you work on this that you get your pitch right. Once you get your notes right, try and hear the notes you're singing with the original notes of the melody. This is the most important part; you need to hear both parts at once. This is where most vocalists fall behind. The reason for this is because whenever you sing harmonies, you're always singing with another person. That other person is usually the lead. Your line must meld with theirs seamlessly. That can't happen if you aren't listening carefully to what they're doing. This listening has to be done as soon as you start practicing harmonies. The best harmony singers I've ever heard didn't just have great pitch, they had great timing, and most of all they had great ears.
A Little Experimentation
The other way to get some harmonies going is to simply start singing and see if you can 'hear' another line, it doesn't matter if the line is 'technically' correct i.e. a correct harmony line moving in perfect parallel with the lead vocal. It just matters that you try and start to 'hear' these things. Again start with a simple line and then start singing lines above (or below) that line. Try to stay above or below the melody; harmony lines as a general rule don't cross the melody. Try as many variations as you can. Remember to try lines below as well as above your original. The value in this is that after you become used to singing harmonies, this is the best way to come up with interesting lines. Line made up are almost always better than lines carefully constructed (this may not be the case in strict harmonies or really involved arrangements) . If used in conjunction with the technical method, you'll find you're on your way to becoming a great harmony singer.
Because some melodies just move around a lot, or don't stick to chord tones, a 3rd or fourth line won't work. Sometimes, because the chords are moving and your line doesn't or vice-versa a moving line won't work. Sometimes when nothing else fails, singing a single note over the entire phrase is best. Not only is it a good idea in some cases, in some genres (like indie rock) a single note above or below the melody will actually sound better (or cooler to your ears). Other styles of rock also like to use one liners like an octave below to a line to thicken it and make it sound darker.
In The Mix
Most of the time a harmony line will play second role to the melody. This usually works the best and like mentioned, it's a great way to bring out that melody. When it comes to having more than one harmony part, you're going to have to go in and do some tweaking to make it sound right. Depending on your harmonies and how many people you have singing any one part, the harmonies are going to have to be mixed right. It's not always all completely even. We tend to like the higher harmony parts better, so they're usually mixed a little higher, or at least heard better. If it's a three (or more) part harmony, be careful with the inner voices. If one of these sticks out too much, it'll sound weird to our ears. Our ear naturally pick up three things. First, we hear the lead and for a lot of people, that's all they really notice. Second, we'll hear the highest harmony, third we'll hear the lowest note and finally we're able to discern the inner voices. To most people those inner voices are almost invisible. A lot of musicians try and pull those inner voices out to make their music more interesting. The point is that unless it's something you want to do on purpose, it'll sound strange to our ears if those middle lines are the most prominent.
Once a special effect, it's now standard for artists to double their vocal line. This is used in every genre of music from pop to rap. There's something special that happens when a vocal line is doubled. Keep in mind that the line has to be sung twice and not just copied and pasted. The latter results in a chorus/phase type effect (or even make the line completely disappear) whereas doubling the vocal will thicken it. Some artists do this numerous times. While effective to bring out a vocal line, it also takes away from the intimacy of a single vocal; the idiosyncrasies and special inflections of the original vocal may get lost. One effect that a lot rock artists like to use is to keep the verse a single vocal line and then double it at the chorus. This really makes the chorus stand out and keeps the intimacy of the verse intact. Remember too that often the harmonies are doubled just as much as the lead. This has the same effect making the harmonies sound bigger (and somewhat smoother) than just the one line. Remember to make the double as close to the original line as possible or you'll end up with a useless mess.
Start Your Harmony Engines
There are so many ways to treat a vocal line. Harmonies are one of the best ways to really pull out a line. Plus, people just love the sound of multiple voices. It's a powerful tool. Try some of the other things mentioned in this article: doubling, octave doubling, alternate lines etc. Even if your genre doesn't generally use a lot of harmonies, you may start something that changes everything. At the very least, you'll create your own unique voice.