Owen spends some time setting out what it means to mortify sin, and makes it clear that the power to so comes from the Spirit, and is given only to believers. Then he gets on to some practical steps, of which there are nine, including "Get a clear sense of... the guilt... the danger... the evil... of the sin", "the first actings of sin to be vigorously opposed", and "Thoughtfulness of the excellence of the majesty of God". These directions make up the bulk of the work.
But when he is done with them, Owen writes "Now, the things which I have hitherto insisted on are rather of things preparatory to the work aimed at than such as will effect it". In other words, think all you want about the guilt and evil of your sin, put as much effort as you can into meditation on the majesty of God, you still haven't even started to mortify sin. For the actual battle against sin, Owen has only two directions, and since one of these is really just a reminder that this is the work of the Spirit, there is actually only one thing to do that belongs to the real fight against sin:
"Set faith at work on Christ for the killing of thy sin".
That's it. Of course, we are used to exercising faith in Christ for the forgiving of our sin, but for Owen it is faith also which will kill it. Setting faith at work here means regarding Christ as the one who will defeat sin in us, actively expecting him to do it, and then waiting for him to come through.
This is as far away from the CBT-disguised-as-sanctification that we often see as you can get.
Two things really strike me about this. Firstly, it will only work if Jesus really is a gracious Lord, and really has conquered sin. It's not a technique, but an appeal to a person with power to exercise it mercifully towards us. It consists in expectation, and waiting, and looking, and longing. In other words, it throws us absolutely on Christ, and not on any source of peace we can summon up in ourselves. (Don't speak peace to yourself until God has spoken it to you, Owen says).
Secondly, this clarifies for me that sanctification, no less than justification, is by faith alone, because by Christ alone. And this is both liberating and glorious.