Right now from what I can see it takes 3 votes to get to the homepage (I checked using the Swequity link, it was at 2 and not on the homepage, after one more upvote it was), but those 3 upvotes have to be in a fairly limited timeframe to be effective. 3 points in 5 hours doesn't cut it, but 3 votes in a half hour or so is enough.

How long it will stay there depends on how many votes and flags it gets after that.

A flag counts as multiple downvotes.