How do I go about manufacturing a homemade drink I love and distributing it to other consumers?

First, you need to check out all the food-related laws to find what standards you need to adhere to in manufacturing the product. The FDA would be the place to start for federal laws, though also look up CA laws.

Second, you should absolutely set up a corporation or LLC in order to protect your family's assets from any liability. Any decent business attorney can help you do this, or you could do it yourself--it's not particularly complicated or expensive. Also get insurance to protect you.

Third, find a good name, one that's not used, for your product and at a minimum protect by asserting copyright in it and using it as a trademark. You can find information on this at the patent and trademark office's website.

From a non-legal standard, you'll need to figure out manufacturing, storage, distribution, marketing, and sales.

If you don't have experience in manufacturing and selling, especially to consumer retail or food channels, and you also don't have much capital, you might also look to partnering with someone who already does this, even for a different type of drink--for example, someone locally with a microbrewery will have much, if not all of the expertise. You'd want to make sure you protect your formula and interests, which means you should consult with a good business attorney on how to do this *before* talking with anyone.