Minor chords have the formula "the tone" + 3 + 4. So if we take make a chord out of E again, it will not be an Em chord (m stands for minor).
Now you have to count 3 tones up from E which is G, and then count another 4 which is B. So the chord Em consists of the three tones: E, G and B.
As you can see, only the second tone is now different. The G# that was in the E chord is now a G in the Em chord.
Since you used the G string to play the G# tone on the 1st fret in the E chord, you can simply remove that finger and play the G string loose, and you'll have an Em chord instead. Everything else is the same, as the change from G# to G only took place on one string. The other 5 strings plays the E and B tones.
If you change between the E chord and the Em chord, you should be able to tell that the Em chord sounds a little sad compared to the E chord.
Sometimes, you will skip some strings. For example in the D chord, you will most often exclude the 2 thickest strings - E and A.
If we calculate the D chord, we start with D, add 4 which is F#, and add 3 which is A.
If we begin with the lowest played string - D, we can just play that loose. On the G string, we need to add 2 tones to get to an A, so place the 1st finger (index) on the 2nd fret on the G string. We need to add 3 tones to B to get to D, so place the 3rd finger (ring) on the 3rd fret on the B string. Finally, we need to add 2 tones to E to get to F#, so place the 2nd finger on the 2nd fret on the E string. As you can see, there are no numbers on the 2 lines representing the lower strings E and A, so do not play those.