You can create a section [color] in your ~/.gitconfig with e.g. the following content
[color]
diff = auto
status = auto
branch = auto
interactive = auto
ui = true
pager = true
You can also fine control what you want to have coloured in what way, e.g.
[color "status"]
added = green
changed = red bold
untracked = magenta bold
[color "branch"]
remote = yellow
I hope this gets you started. And of course, you need a terminal which supports colour.
Also see this answer for a way to add colorization directly from the command line.
