Anytime you play a note, skip a note, and play the next note, you are playing a 3rd. The following are all 3rds. They're not the same quality (major, minor, etc.), but they are all 3rds of some kind.
CE
DF
EG
FA
GB
AC
BD
When you put at least two of those 3rds together, you form a chord. Chords are simply multiple notes played at once. Example:
C-E + EG = CEG
Notice how the two 3rds are formed. The last note of the first 3rd is the first note of the last 3rd. This is how 95% of chords are formed. This is also how you can tell what the root of a chord is, by stacking it in 3rds.
Are you familiar with the 1-3-5 chords, which is the 1st chord built off the 1st scale degree? Do you know how to get the rest of the chords? Well, the same process you went through to get the 1, 3, & 5 is the same process you go through to get the other chords. Notice with 1, 3, & 5 how you skipped 2 & 4. Well you are going to do the same starting on the others. Here is an illustration:
1 (skip 2), 3 (skip 4), 5
2 (skip 3), 4 (skip 5), 6
3 (skip 4), 5 (skip 6) 7
4 (skip 5), 6 (skip 7) 1
5 (skip 6), 7 (skip 1) 2
6 (skip 7), 1 (skip 2) 3
7 (skip 1), 2 (skip 3) 4
When you put the notes altogether, it looks like this:
1-3-5 = major 1 chord
2-4-6 = minor 2 chord
3-5-7 = minor 3 chord
4-6-1 = major 4 chord
5-7-2 = major 5 chord
6-1-3 = minor 6 chord
7-2-4 = diminished 7 chord
If you do it right, you should hear those chord qualities (major, minor, etc.) above. Now, as far as the notes go, you will only use the notes of the major scale for these chords. So, using the scale degree formula above, here are all the chords in C:
C major scale: C = 1 D = 2 E = 3 F = 4 G = 5 A = 6 B = 7
1-3.5 = CEG
2-4-6 = DFA
3-5-7 = EGB
FAC = 4.6.1
GBD = 5-7-2
ACE = 6.1.3
BDF = 7.2.4
When we refer to chords built on scale degrees, the chords are now referred to with roman numerals. The lower case numerals are for minor chords and the upper case numerals are for major chords. The diminished vii chord is also in lower case. There are lots of technical terms (tonic, major, minor chords, and diatonic scale) to help grasp chords that lead to understanding chord structures . I hope this simple explanation helps.