The prompt is set by the environmental variable called PS1.  To display the current setting, I can use:

echo $PS1

The system-wide setting of the prompt (for all users on the system) is in the file /etc/bashrc which on my system
contains such a line:

PS1="[\u@\h \W]\$ "

To customize the prompt, I can edit the file /etc/bashrc (as root) and insert almost any text inside the quotation marks.
Here is the meaning of some special codes I may also choose to use:

\u   -    username of the current user (= $LOGNAME),
\h   -    the name of the computer running the shell (hostname),
\H   -    entire hostname,
\W   -    the base of the name of the current working directory,
\w   -    the full name of the current working directory,
\$   -    display "$" for normal users and "#" for the root,
\!   -    history number of the current command,
\#   -    number of the current command (as executed in the current shell),
\d   -    current date,
\t   -    current time (24-hr),
\T   -    current time (12-hr) - bash 2.0 only,
\@   -    current time (AM/PM format) - bash 2.0 only,
\s   -    name of the shell,
\a   -    sound alarm (beep),
\j   -    number of jobs the user has,
\n   -    new line,
\\   -    backslash,
\[   -    begin a sequence of non-printable characters,
\]   -    end a sequence of non-printable characters,
\nnn -    the ASCII character corresponding to the octal number nnn.
$(date) - output from the date command (or any other command for that matter),
 

Here is an example on how to add colour. See the next chapter for details about colour:

PS1="\[\033[1;32m\][\u@\h \W]\$\[\033[0m\] "