As an example lets harmonize C major scale. We all know that it can be played with notes like this

C D E F G A B C

It can as well be played with chords like this:

C – Dm – Em – F – G – Am – Bdim – C

Up, thats harmonization! Chords are very basic so I will do not think it is necessary to tell you how to play them. Playing this exercise name the chord you are playing and also the scale degree, from which it is build.

C	Dm	Em	F	G	Am	Bdim	C
I	ii	iii	IV	V	vi	viio	I

Pay attention that minor chords are marked with small roman numerals. This is a common practice, so get used to it. Knowing these scale degrees is the key to transposing the songs from key to key, taken that you know the chords in a given of course.

You can harmonize same scale in a number of different ways: use only triads, 7th, 9th, 11th, 13th chords, play in different positions (great exercise for expanding your fretboard knowledge). You can harmonize any other scale in the same way. You might need to refer to some music theory book for help though.

Homework: harmonize major scale in other keys. Try at least F, G, D, A, E and B using most simple chords staying as close to the open position as possible.