Given that you're trying to save an object's properties to a database, you may want to look at an ORM tool like Linq2SQL or NHibernate instead. I don't know your situation, so those tools may be overkill. If so, just use reflection as the other responses have suggested.
Object/Relational Mapper (ORM) tools do exactly the type of thing you are trying to do. They take your classes and map them to your database entities. ORMs handle more than just your simple property -> database column example. They generally can handle relationships, lazy or eager loading, and advanced queries.
Linq to SQL (also known as Linq2SQL) is built-in with the .Net 3.5 framework and allows you to use Linq queries against the database instead of straight SQL. You also get to use a drag-and-drop designer in Visual Studio to create the mappings between the database schema and your classes.
NHibernate is a free open source ORM tool you can find at
https://www.nhibernate.org/[
^]. It's mature and very powerful, but definitely has a steeper learning curve than Linq2SQL. There are many ways to do the mappings with NHibernate. You can chose between xml files, a fluent interface, or attributes applied to your classes. Queries can be make using the NHibernate criteria api, HQL (similar to SQL), or even Linq.
Naturally, there is far more to any ORM than what I can explain in a quick answer, so I recommend you Google ORM, Linq2SQL/Linq to SQL, and NHibernate for more information.