A chord progression is just 2 or more chords played with one chord leading or progressing to the next chord. The ultimate goal is to get back to where you started. To name the progressions we use numbers which represent the scale degrees of the major scale of the key you are in. Example:
2-5-1 progression
Key C
Key C scale degrees: C=1, D=2, E=3, F=4, G=5, A=6, B=7
2-5-1 progression in C: D, G, C
Now, to figure out your chords, the easiest way is to build of the notes of your progression, which are the scale degrees of the major scale of the key you are in: Here are all of them in C:
1 = C-E-G (major)
2 = D-F-A (minor)
3 = E-G-B (minor)
4 = F-A-C (major)
5 = G-B-D (major)
6 = A-C-E (minor)
7 = B-D-F (diminished)
Now, let's plug them into our 2-5-1 progression:
D / D-F-A
G / G-B-D
C / C-E-G
(repeat)
Now, let's play the same thing, but we are going to use inversions of the chords so that you don't have to move your hands:
D / D-F-A
G / D-G-B
C / E-G-C
(repeat)
D / F-A-D
G / G-B-D
C / G-C-E
(repeat)
D / A-D-F
G / B-D-G
C / C-E-G
(repeat)
It's that easy. Any questions?