OK, super easy open (though Step 1 is not really legal) ... Step 1 - get a piece of mail out of their mailbox. Bring it to them that night, saying it got dropped off in your mailbox. You can be a little funny about it, joking that you have enough bills of your own without the mailman trying to get you to pay theirs. Beyond that, don't push too hard, but it makes the introduction. From there, you can slowly build rapport as you see each other (not to mention being able to recognize them without being creepy), and you have a conversation starter for later.
Step 2 is to throw a party. Invite a few friends, and them. Now you've got the situation where (if they come) you can actually start to work your pickup. You can skip step 1 if you get a chance to break the ice another way, or you can skip it altogether if youre comfortable going up to them and just inviting them.
I used the party as a way to instant-date my neighbor when she (HB8) and her friend (HB9) invited me to our apartment pool with them (I opened them when I saw them talking and referenced an earlier time my neighbor had been locked out of her car). While at the pool, I texted another neighbor and suggested we fry some fish and invite some friends over. In short, I threw an entire party to kiss close my neighbor. Probably would have gone farther, but she ended up deciding that she didnt need to get involved with a recently divorced guy.