i absolutely agree with vanille's response, and maybe i can add a little more insight from my personal experience.
just about 6 months ago i discovered that my husband had had 2 affairs in the previous 3 years. i felt violated and betrayed on every level, and continue to process my complicated feelings about myself, him, the other women, and our relationship. in the aftermath of that crisis, he made clear that he does not want a monogamous relationship, so we are exploring the options.
TELL YOUR WIFE! AS SOON AS POSSIBLE!
maybe do some more research online so that you've got some idea of how she may react. my husband didn't think it would be such a big deal to me--was he ever wrong!
be prepared to go to relationship counseling--i don't think my husband and i would have made it this far without doing so.
be prepared to put a good amount of time and energy into reading and talking about your relationship (past & current) BEFORE you bring up polyamory. i have found it VERY difficult to think about opening up our relationship whilst healing from what felt like a very traumatic rift for me.
be prepared to at least temporarily stop seeing your girlfriend. your wife will likely be VERY angry at both of you and it will likely be a major distraction to dealing with your relationship issues if she has to deal with all the issues surrounding this other woman at the same time.
make sure you provide lots of support to your wife and kids in what will likely be a difficult, tumultuous time--don't forget to give the kids lots of attention, they will feel the anger and tension and may be concerned. don't rely on your wife to take care of home and kids as usual--she may find it difficult to take care of herself for a while.
that's not an exhaustive list, by the way, and i realize it is completely subjective. your wife may surprise you in one way or another...
but if you want an open, honest relationship with ANYONE, you've got to start immediately with yourself and your wife. the sooner, the better.
best wishes to you and yours!