How to make citations appear within square brackets [ ] instead of parentheses ( )?

You can simply say

\setcitestyle{square}

in your document preamble (see natbib documentation, section 2.9).

However, if you're using the class for a submission to an IEEE conference, leave as they want.

The reason why you are getting citation numbers inside parentheses instead of square brackets is that in the class file you use, the package natbib is loaded with the option round, see line 51:

\usepackage[round, sort, numbers]{natbib}

Just replace this line with

\usepackage[sort, numbers]{natbib}

save your class file, compile your .tex file and you should get square brackets. Alternatively, simply adding \setcitestyle{square} in the preamble of your document without modifying the class file itself should work.

Note, however, that you may also have to edit the bibliographic style to change the style of the bibliographic number (at present, is it enclosed by parentheses or square brackets?) for each item in the Bibliography section.