In previous posts you learned two chords, G and C. Once you're comfortable with them both it's time to start putting the two together. This post will get you playing the two chords one after another. As usual, start by practicing slowly; the worst enemy of the beginning guitarist is haste.
Start by placing your 3rd finger slowly in the position for the G chord. Don't press the chord just yet, rest it lightly on the string at the 3rd fret. Now, check that you're breathing in and out calmly. This might sound strange, but often in an excess of concentration when learning something new I find that I stop breathing.
If you're breathing calmly then you can try slowly lifting your 3rd finger. Then place your 1st finger on the 2nd string for the C chord. Again, just rest it lightly on the string. Repeat the movement in reverse: lift your 1st finger and place the 3rd finger for the G chord.
Practice these two movements, nice and slowly, and remember to breathe all the while. As you become comfortable and can accurately perform the two movements, you can try pressing down the string for each chord.
When you're comfortable with pressing down the strings add a strum. One for each chord is fine for starters. As you gain skill and confidence you can try strumming each chord four times.
Congratulate yourself. You're well on the way to start playing songs...