Positive reinforcement, not encouraging bad behaviours, not letting them sleep in your bed, controlled crying, discipline, and love unabounding.... yep, this is exactly the approach that I took with my puppies, and I now have two fantastic, well-behaved, grown-up dogs :lol: I'm kidding, of course. But whenever I have had difficulties with my partner's son, I have turned back to the basics of good dog training, and it has not failed me... yet
On a different note, you have got some great advice on this thread about what to do for your newborn (congrats, by the way!). But at the same time, I would encourage you and your partner to discuss how it might change your relationship - your priorities, your time for each other, the effort you put in to make each other feel special - and do your best to continue doing at least some of this. The best gift that my parents ever gave me was that of showing their kids the stability, functionality, and "specialness" of their own relationship by putting their efforts not only into us, but also into each other. It taught us boundaries, responsibility, and how good things can be between a husband and wife.
My partner and I try to model similar behaviours in our life and family unit, and his son (now 13) has expressed to me how good it has been for him to see his dad so happy, and in a mutual, respectful successful relationship, as opposed to the number of other broken relationships he has had to witness. So far, just like it was a gift from my parents to me, I'm really glad I've been able to pass something positive onto both my partner, and just as importantly, his son.
Good luck!