How can my sim own a business?

Hello @LadyHawke27 !  Click on the phone and then the "household" button to get that option.

This will prompt you to buy a property for your business.  So make sure your sim has enough funds to buy the property and to build it, if you haven't already set up a business on the lot you're buying.

Edit: Just to clarify you'll need...
- Get to Work EP to have the Retail store option
- Dine Out GP  to have the Restaurant option
- Cats and Dogs EP to have the Vet Clinic option

I will say, there are a few things to consider once you buy it as well:

• Your household and business funds will be separate, so once you are on your business lot, make sure to transfer funds from you household to the business so you can actually buy things.
• If you want a special type of business, you have to have certain objects for it to function, the game will tell you what under "lot type" so pay attention to that or it won't work. For example: retail stores require a register, and restaurants require a chef station, waiter station, and a bathroom.

Businesses are loads of fun with how you can pretty much sell whatever you want, so have fun!

In the bottom right of your screen when playing a household, there should be a till (cash register) icon which if you click offers you the ability to buy a business; however it does require the Get To Work pack if I remember correctly. If you own the pack but still can't find the icon, you can use the computer and buy a business through the household section.