The thing you need to learn is what notes are in a chord. It doesn't matter how they are placed in a chord; it still is the same.
The basic chords are built on thirds. So, take the notes you have and try to put them in order of thirds. We need a Root, a third (major or minor) and a fifth.
The fist chord you have is: G-E(bass clef) C-G (treble clef).
The notes we have are G,E,C and G (again; no need to mention it twice)
Let's take the lowest note and see if we can built a chord of thirds on top of it.
- G-E is not an third or fifth (interval).
- G-C isn't either.
So, our chord doesn't have G as a root. Let's take E and repeat the same process:
- E-G is a third (so far so good)
- E-C is a sixth (this isn't good; see above, we need a fifth here).
So, we shall take the note that is left and check the same thing:
- C-E is a third (major one)
- C-G is a perfect fifth.
So, as you can see, we have successfully built a major chord. The C major chord.
Now that we've found what chord we have, let's see what kind of inversion we have. If the third of the chord is in the bass, the chord is in first inversion; if the fifth of the chord is in the bass, the chord is in second inversion. If the root is in the bass, the chord is in root position.
In your example, the G (fifth of the chord) is on the bass, so the chord is on second inversion.
The same goes for all the other chords in your examples.