The first three months with both of mine were pretty easy, relatively speaking. Eat, sleep, poop, cry, lather, rinse, repeat (them); cry, sleep, eat, cry, write, shower occasionally (me). I did my Masters degree around the birth of my second; turned my rough draft of my thesis in the week before his due date, did my revisions over his head during his marathon nursing sessions, defended when he was three months and then gave up life for the next six.
Once they woke up out of the fourth trimester potato stage, things got a lot more interesting. In that "may you live in interesting times" kind of way.
(I was still extremely lucky in that we have one-year mat leave where I live, and my first was in day care while I was home with the second. I know a huge number of people don't have that luxury. Privilege firmly acknowledged.)
So writing during naptimes, a few sentences here and there once they were down for the night. A lot of writing during lunchtimes at work, and writing on my phone during bus rides when I had kid-free bus rides. I wrote almost an entire novel-length fic on those bus rides, syncing Docs-on-the-go to dropbox and picking up lines here and there when I had a chance to breathe. It was my escape.
Now that they're in school and preschool, and have predictable bedtimes, life is much easier to plan. I write after they go to bed, and my work schedule is erratic so that I often end up with days off while they're at school and partner is at work. Once the basic chores are done? I take advantage even when I don't feel like it.
My last couple of weeks have been like pulling teeth to get words on the page, but there's a lot more motivation to 'git 'er done' now when I know they're going to be home all day every day on Christmas break, starting in a few days!
The one thing impossible to write while the kids are awake? Sex scenes. Even when they're in a different area of the house, I just can't. Those get saved for days off and evenings.