Obviously the best way to make some Simoleons is to join a career track.  But really, how boring is that?  (Pretty boring.)  Here are some other ways to make it rain!

1. Gardening

Obviously you can grow produce and sell it.  (Tip: instead of hauling everything to the grocery store to sell, just click and drag it from your Inventory onto the "sell it" square.)  The better the quality of your produce, the more money you earn.

But I'll tell you what: my Sims are earning a fortune from their five Money Trees!  I think the best strategy is to sprint to a high enough Gardening level to grow this tree.  Then plant as many of them as you can find.  Each Money Tree will eventually drop a Money Tree seed, so you can really start your grove with just one.

2. Painting

The better your painting skill, the more your paintings are worth.  Trade in happiness points for the "Artistic" trait, and take a painting class to improve your skill.  Note that if you hang onto the paintings they will increase in value.  Particularly after the Sim who paints them has died!

3. Playing Guitar

Once you get good enough at the guitar, you can "Play for Tips."  By the way, this works best if you do it in public, during the day!  You don't earn much, but you improve your skill while you play.  And it's nice to get out of the house once in a while.

4. Hacking

If your Sim has the "Computer Whiz" trait, they can earn a little money from hacking on the computer.  From peering over their shoulder, I decided that your Sim "hacks" by logging into their own bank account, then running a script that logs them into some other bank customer's account.  This explains why the amounts you earn are random (and usually quite small.)

5. Fishing

As with gardening, you can sell the fish that you catch.  Fishing gives you a better turnaround on your investment, since you start catching fish from your very first cast - although it can take many days for your plants to begin to bear fruit.  However, fishing also takes a lot more of your Sim's active involvement, unlike gardening where the plants grow while you go do other stuff.  

6. Gems

Don't even try to earn money by hunting gems unless you have the Collection Manager.  This Lifetime Happiness Reward will show you where all the gems are - so all you have to do is go through the surprisingly difficult task of clicking exactly on the gem to tell your Sim to go collect it.

I read a breakdown somewhere that if you're after money, your best bet is to sell the gems raw.  Gems command a higher price after they have been cut, but the cost of having them cut really eats into your profitability!  The same goes for smelting ores - it's better to sell them in their raw state.

7. Investing in a Business

This can take quite a bit of scratch up front, but it really pays off in the back end!  One of my Sim families has a stake in the bookstore.  You just click on the title in their inventory when it's time to collect the $2000 earnings.  This seems to happen about every two weeks or so.