Well, you sing a melody from a scale. The scale you use depends on the chords that are used. Use the reverse scale finder link at the top of the page ro find out what scale though chords equate to. For example if you had (really easy example)... D, G and A major chords, and you wanted to know the scale, you basically add up all the notes from those chords...
D, F#, A, G, B, D, A, C#, E
ok... rearrange from low to high, and ignoring notes that appear twice...
D, E, F#, G, A, B, C#
hey presto! the D major scale. Using the Reverse Scale Finder works in the same way, but it's loads quicker!
Harmonising (us Brits spell it with an "S" rather than a "Z") refers to adding notes above or below a melody (or a scale). For example, you can take the D major scale, and add notes a 3rd and a 5th (3 and 5 scale degrees - D, e F#, g, A) higher:
D E F# G A B C# D
F# G A B C# D E F#
A B C# D E F# G A
This gives the chords Dmaj, Emin, F#min, Gmaj, Amaj, Bmin, C#dim, and Dmaj again.
If you added the 7th above the scale, then you get Dmaj7, Em7, F#m7, Gmaj7, A7, Bm7, C#m7dim5. The last chord is a bit weird. It's got a diminshed 5th, and a minor 7th. It's also called "C# half-diminished 7th". If the 7th was a diminished 7th (ie a semi-tone lower) then the chord would be a diminished 7th.
For examples of harmonising a vocal melody, listen to some of RHCP's newer stuff, or if you like things a bit darker, then check out Alice In Chains. Jerry Cantrell was awesome at harmonising vocals, and a kick-ass guitarist as well :D http://www.youtube.com/watch?v=99-lD2Dn6Q4 this song has good vocal harmonies in the chorus (0:39), but more or less every AiC song contains similar intense harmonies.
For bands that harmonise a guitar riff/solo - Iron Maiden, Thin Lizzy, Mastadon, etc. Basically any band with more than one guitarist. Oh, but I'm not including Razorlight in that!
Many bands with one guitarist can still have harmonised solos, by overdubbing parts on studio recordings, or using a pitch shifter, a device that takes the pitch of a signal and mixes it around so it's a 3rd or a 5th or an octave higher, depending on how you set it. You can also buy a "Whammy" pedal, made by US company Digitech. Similar to a pitch shifter, but you can use the expression pedal to control the pitch within a range (1 octave up from original note, 2 octaves up, etc) and slide between notes. For example, the guitar in the verses of Calm Like A Bomb by RATM.
Hope this helps.
