Well, understanding the tuning is very important when you want to progress to more color chords. So the basic C6th tuning has the major triad notes that make up a C chord, plus a 6th tone.  So looking at this chart will show you where to find several possibilities for a C7 (dom). The chart shows the open string note and what number tone it is in the key of C.  For a C7 you will have any triad note plus the dom7 note.

(Fret)
0      1    2    3    4    5    6    7    8    9    10   11   12

G(5th)___________7_____________________________________________5
E(3rd)___________5___________________________________9_________3
C(1)_________________________________5_______________7_________1
A(6th)_7_________1___________________3_______________5_________6
G(5th)___________7_____________________________3_______________5
E(3rd)___________5_______________7_____________________________3
C(1)___________________________________________________________1
A(6th)_7_________1_____________________________________________6

The triad of C is 1, 3, and 5. So you can see on the 0 fret you can have any combination triad note with the bar on the 1st fret for the 7th tone added. And on the 3rd fret you have a root and 5th and 7th to choose from.  Looking at the 7th fret, you have part of a C triad and add the slant for the 7th tone. On the 10th fret there is the 9th with the 7th and a 5 there for a C7/9 chord, or combine any of the 10th fret notes with the slant for the 3rd tone, and you have C7. So make yourself some charts like this for any tuning you are using and chart out the notes and where they lay and you can find all the possibilities in chording that you desire.