What do you do if something you buy on eBay never arrives?

You would need to start a "dispute", either through PayPal (if you paid that way) or through eBay's own resolution center.

The seller then needs to prove to PayPal (or eBay) that the item was delivered to you by providing them with an online-trackable delivery number. If they are unable to do that, you should get a full refund of your money.

There are strict timeframes relating to "disputes" - check in the help section of your own local PayPal/eBay site to confirm what those are.