The quick answer: their parents give them one.
…If only paychecks and mansions on the beach worked that way.
But, for Real
A diploma is nothing more than a document that states that its bearer has met the requirements for graduation from a program of learning. It's issued by the person or institution responsible for supervising a person's education. And if you're a homeschooling parent, that means you.
This is why it's a good idea, particularly if your child is planning to continue on in a post-secondary institution of some sort, to spell out your requirements from the get-go and help your child stay on track to meet them. You may also want to make sure you stay on top of record-keeping so that you have substantial evidence—for yourself, your child, or anyone else who ever requests it—of the work your child has completed in order to earn that diploma.
For more on record-keeping and organization through the high school years, check out our articles that just so happen to be on those very topics:
The Exception: a Supervising Institution
If your child enrolls in a correspondence program, a charter school, or an official organization like NARHS or Penn Foster, that institution will issue your child's diploma once all requirements for graduation have been met. Whether the place is online or brick-and-mortar, it's important to stay on track of their documents as well as your own.
Why? Because in these cases, even though you are still homeschooling, the institution has taken responsibility for supervising your child's education (in an official, legal sense, at least). And that means that it—not you—will issue your child's diploma.
But where do homeschoolers get the actual, physical diploma?
There are a lot of options here, and they depend on just how formal you want to get.
The super casual route: purchase a blank certificate from a stationery store and fill in the necessary information.
Boom, diploma complete.
For a slightly more formal approach, you could create a diploma using word processing or publishing software and either print it at home or have it printed at a copy shop on a nice cardstock.
Here's another example. At the New School in Kennebunk, Maine, high school juniors take on the role of "graduating" their seniors by crafting them individual diplomas and graduation hats. Check out the graduation pictures on their "About Us" page for a peek at some graduates getting theirs.
For a diploma that looks every bit as formal and official as the ones that are given out during traditional high school graduations, you may want to use an online service such as Homeschool Diploma, which does a beautiful job and offers diploma covers as well as wallet sized copies (only available if you purchase a full-sized one), as well as other graduation supplies.
The HSLDA also offers diplomas and cases through their store.
Bottom line: whether you're out for a diploma for application purposes or to highlight your child's achievement of 12 (or so) years of home learning, you've got options. Lots of 'em.