You can use either "=" or "==" operators for string comparison in bash. The important factor is the spacing within the brackets. The proper method is for brackets to contain spacing within, and operators to contain spacing around. In some instances different combinations work; however, the following is intended to be a universal example.
if [ "$1" == "something" ]; then ## GOOD
if [ "$1" = "something" ]; then ## GOOD
if [ "$1"="something" ]; then ## BAD (operator spacing)
if ["$1" == "something"]; then ## BAD (bracket spacing)
Also, note double brackets are handled slightly differently compared to single brackets ...
if [[ $a == z* ]]; then # True if $a starts with a "z" (pattern matching).
if [[ $a == "z*" ]]; then # True if $a is equal to z* (literal matching).
if [ $a == z* ]; then # File globbing and word splitting take place.
if [ "$a" == "z*" ]; then # True if $a is equal to z* (literal matching).
I hope that helps!