1) Similar to other clothing , when putting on shoes, the right should be put on before the left.
2) When tying shoes the left comes before the right. This is because tefillin are tied on the left arm indicating that for tying the left takes precedence. Since a lefty wears tefillin on the right arm, they would tie the right shoe first. R’ Shlomo Zalman Auerbach z”tl ruled that being that women do not wear tefillin, they should also tie the right shoe first.