Combinatorial group theory by Lyndon and Schupp is the classic text to be introduced to small cancellation groups. There is also Geometry of defining relations in groups by Ol'shanskii which introduces small cancellation theory and has generalizations which where used to prove the existence of Tarski monsters.
For cubical small cancellation Wise has a section in Riches to RAAGS, but I have not read it, but looks pretty good.
Graphical small cancellation Ollivier has a paper On a small cancellation theorem of Gromov which gives a combinatorial proof of the basic small cancellation results, and I think having some knowledge of classical small cancellation theory would make this basically self contained. It is an important step in the proof that there exists finitely generated groups which do not coarsely embed in Hilbert spaces, by being flexible enough to make groups contain a sequence of expanders.