What can a person actually do to save themselves?
According to the context, a person can do nothing to save themselves. Like Israel at the Red Sea, they are told to stand still and not try to build a bridge or find something to float across. Salvation happens only when God moves in and performs the miracle.
Les teaches that the sinner cannot cause the metamorphosis; God is the One who transfigures a hell-bound sinner into a heaven-bound saint. All a person can do is stand stark naked before a Holy God and admit they cannot even move from where they are. As Israel stood still at the Red Sea, the unbeliever must come to that same place and do nothing until God moves in and performs the miracle of salvation. That miracle creates within us a whole new mind, will, and emotion; the personality has to be totally recreated, and old Adam has to die.
And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.