Just because you have an opportunity to meet your new neighbors after you move into the neighborhood, doesn't necessarily make it easier to do. Some of us are shy, while others of us are more concerned about privacy - both ours and our neighbors.
Careful ObservationCheck out your neighborhood, noting those who seem to have kids (toys out front, loud screams from the backyard and parents frantically trying to get small people into a van along with sports equipment), those who are elderly, those who seem to be always in the garden or even those who only seem to come out at night (although they're more difficult to meet, unless you are also a night owl).
If you can find some common ground - you both have kids, your mother is elderly or a friend talks about her garden a lot even though you yourself don't possess a green thumb - this will make it much easier to approach the person.
The key in careful observation is to not be obvious about it nor act stalker-ish. Some people may feel a little strange if you seem to know too much about them.
Make Your MoveWe all have busy lives, so make sure you only approach your neighbor when it seems like it might be a good time. Avoid dinner, breakfast and early mornings (unless they're already up and outside) and when they're getting in their car. Usually, if someone is leaving or coming home, they have an agenda and plan and don't necessarily appreciate the interruption.
What to SayIf you go back to what you've observed about your neighbor you can start there. Just make sure that it's pretty casual sounding and that if it's at all detailed, that you explain how you uncovered this phenomena. For example, if you see your neighbor scrambling into her van with two girls in tow, one with a baseball glove and the other in a tutu, then you could approach your neighbor and asked about community softball for your own child or where your child might take ballet lessons.
What if We Have Nothing in Common?No problem. There's absolutely nothing wrong with just walking up to the front door, and introducing yourself. Let them know that you just moved in and where you moved from. If that still feels uncomfortable, then ask about garbage pick up or recycling centers in the neighborhood. Remember, while you think you might not have anything in common, you do: you live on the same street, in the same neighborhood. That's enough to start any conversation.
Be Friendly, But Not InvasiveI had a neighbor once who introduced himself, then misconstrued my friendliness to be a sign that I wanted an extended conversation. I didn't and I tried to avoid him from then on simply because I was always afraid of "getting caught" in a lengthy discussion. My rule is always to keep the talk short, unless it's naturally progressing, and to allow the neighbor to make the move for an extended visit. If they're interested, they'll say so or even invite you in. Leave it in their hands.