@Scott88 - I'm not going to pretend for a second that it's easy. Or that it works straight away.
@Friday has given some great links to follow up on.
It's definitely a balancing act, between paying a bit of attention to your thoughts and making a conscious effort to not just let those thoughts run amok and ruin the daily experience of raising a child, but also once you've acknowledged those thoughts, also remembering to bring your mind back to whatever it is that is going on around you, outside your head.
For me? The process gets really cyclical: acknowledging thoughts, and back to focusing on the moment; and the thoughts come back and I'm having to acknowledge them again, and back to the moment; rinse and repeat.
When you first start out practicing this skill, your head is going to throw up a whole heap of resistance. Why are you trying to challenge me, Ragdoll? I'm keeping you safe. These thoughts are reeeally important. Pay attention to me, Ragdoll. No, seriously, you have to keep thinking these thoughts... And on, and on.
You get tired and frustrated of it pretty quick, so practice when you can, but don't drive yourself batty in the process!
But remember that your hrain is getting bored of throwing the same thoughts at you over and over and not getting the attention it's after. Your brain gets sick and tired of trying to get your attention and not getting anywhere. And eventually, it puts less and less vigour into the thoughts, and they (gradually) start coming and going with a lot less effort. Your brain, even more than throwing these thoughts at you? Wants to stay busy. It loves being engaged. So it will eventually start to look elsewhere for ideas and thoughts that you're going to pay attention to.
Our brains never really shut up. But we can learn (and it is a learned skill, not a natural one) how to pay it attention, or not.
But like I said, it's not easy changing these patterns. So don't feel like "This isn't working" if the thoughts continually come back at you. They make sense, and it really is okay that those thoughts are there.