Right lets first go basic,

For a m3 harmony note move up 3 frets
Maj3 move up 4 frets
5th move up 8 frets

Thats simple basic, of course you can then octave them up or down

Now a bit more complex but if you know your modes you are laughing

Going through the modes

IONIAN
DORIAN
PHRYGIAN
LYDIAN
MIXOLYDIAN
AEOLIAN
LOCRIAN

So if we are in the key of A IONIAN (Major scale)

A B C# D E F# G#

You'll have

A IONIAN
B DORIAN
C# PHRYGIAN
D LYDIAN
E MIXOLYDIAN
F# AEOLIAN
G# LOCRIAN

So you are playing the Ionian pattern to harmonise in 3rds you'll play the C#Phrygian pattern over it and so on

A B C# D E F# G# ----------- C# D E F# G# A B

5ths will be Mixolydian

A B C# D E F# G# ---------- E F# G# A B C# D