All the options for persisting value objects mentioned in the previous answers - such as flatting the value object properties as columns of the entity table they belong to or persisting them in a separate table by including a unique id for the data model - are valid and well explained. And of course those options are usually applicable independently of the specific underlying database technology which is a great plus.
But I think it is at least worth to mention some other options which in many cases can be sufficient and easy to implement:
Store value objects in JSON representation
It depends on your technology constraints of course but nowadays many databases as well as ORM solutions even provide built-in support for JSON representation. Some even including search options. If you don't expect a huge amount of items you can even use this approach for lists of value objects inside entities by persisting this list as JSON collection of objects directly in the entity table.
Alternatively to JSON there are of course other formats supported (such as plain text or XML) but from my experience I find JSON to be most comfortable.
Use a document-based storage solution
It might also be worth to mention that choosing a document based-database technology - such as MongoDB - also provides new options for persisting domain model entities as it at allows to persist an aggregate as an entire document including all its child entities and/or value objects.