The verbal descriptions take a while to read through to get a feel for the expected results for fopen modes. This csv table can help break it down for quicker understanding to find which mode you are looking for:
Mode,Creates,Reads,Writes,Pointer Starts,Truncates File,Notes,Purpose
r,,y,,beginning,,fails if file doesn't exist,basic read existing file
r+,,y,y,beginning,,fails if file doesn't exist,basic r/w existing file
w,y,,y,beginning+end,y,,"create, erase, write file"
w+,y,y,y,beginning+end,y,,"create, erase, write file with read option"
a,y,,y,end,,,"write from end of file, create if needed"
a+,y,y,y,end,,,"write from end of file, create if needed, with read options"
x,y,,y,beginning,,fails if file exists,"like w, but prevents over-writing an existing file"
x+,y,y,y,beginning,,fails if file exists,"like w+, but prevents over writing an existing file"
c,y,,y,beginning,,,open/create a file for writing without deleting current content
c+,y,y,y,beginning,,,"open/create a file that is read, and then written back down"