One thing I've done a couple times at work is to offer to help someone move. Anyone who has moved to a new house knows an extra pair of hands are pretty much always welcome, so as long as you're on somewhat friendly terms, they'll accept your offer. After that, you're friends. But since people don't move every day, then you'll need another 'ice-breaker'. Something simple like loaning a DVD or some other small thing that comes up in conversation. They appreciate you thinking of them and trusting them with something of yours. Course, this assumes they'll give it back. Hopefully the person you want to be your friend is someone who gives things back they borrowed.
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Everything would be better if you were in charge.