How do I delete the newline from a process output?

Assuming it is stored in a variable output-string, the final newline at the end can be removed this way:

(substring output-string 0 -1)

With the shell-command way, it would look like this:

(substring
  (shell-command-to-string "git rev-parse --show-toplevel")
  0 -1)

I think you can do

(replace-regexp-in-string "\n$" "" 
              (shell-command-to-string "git rev-parse --show-toplevel"))

If you only want to remove a newline at the very end of the output, use

(replace-regexp-in-string "\n\\'" "" 
  (shell-command-to-string "git rev-parse --show-toplevel"))

The accepted answer also replaces pairs of newlines ("\n\n") in the output by single newlines ("\n"), because $ matches at the end of the string or after a newline, while \\' only matches at the end of the string.

If You are OK with awesome external package.

use s-trim

ELISP> (shell-command-to-string "light -G")
"60.00\n"

ELISP> (s-trim (shell-command-to-string "light -G"))
"60.00"