Tap on everything
In Kim's world (probably both in-game and in real life), money grows on trees, and on fire hydrants, and on restaurant sandwich-board signs, and in birds. Each neighborhood you visit has two or three hotspots — usually signs, birds, bicycles, skateboards, and newspaper machines — you can tap on to get extra drops.
Often you'll get cash and experience points from these drops, and occasionally you'll get energy, so it's a great way to pass the time if you're waiting for your energy to replenish. Plus, your energy replenishes quicker if you tap on dropped items to pick them up. Each item picked up knocks about five seconds off your energy-replenishment timer.
Get free cash/stars
There are a few ways to get free cash and stars in the game. The most straightforward way is to go to the currency store: Both the cash store and the star store have an option for getting free currency. Watching ten-second videos will get you $10 cash or one star, but there are only so many videos you can watch. However, if you tap "other offers," you'll be taken to a list of offers you can complete (usually app downloads) to earn cash and stars. Most of the offers are free (a few are not) and easy to complete, and you get your payout within a few seconds of completion.
You can also earn stars by inviting friends from Facebook and by real-life tweeting about your in-game success. The Facebook invites are pretty straightforward: You get two stars for every friend who signs up (who's not already playing the game). Tweets go out after every milestone ("I'm a C-Lister!"), and will earn you two stars apiece. However, tweets are automatic and un-editable, so you may not want to connect this to your main Twitter account (or your office's Twitter account). I just made a fake Twitter account and connected to that; now I get two stars for every milestone, and I don't have to worry about annoying my (real) followers.
Don't date people
One way to increase your fame in the game is to date people who are more famous than you. But it's not worth it, and there are much easier ways to get to the A-List.
Dating people costs money right off the bat. First, you're probably not going to be able to get a date with someone who's more famous than you unless you "charm" (aka bribe) them with stars. Bribes are expensive — expect to shell out five or six stars per person. And you can't really afford to be spending those stars on randos, because most of the cute clothes cost at least 50 stars.
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