How can I release a winform application to a user that takes advantage of a local sql database. I would assume that I need to install the database during some kind of setup phase, but is this kind of thing possible? Is there a free version of tsql that can be used in this way? Mysql?
SQL Server Compact Edition is suitable for this. It has some limitations in that it does not support the full set of functionality that SQL Server supports (ie. stored procedures is one example), but it does mean that you don't need an installation of SQL Server to use it. If you are only using the database as a "bit bucket" to store and retrieve data, then it should suffice.
Another alternative is to use SQL Server Express Edition. This does require installing a proper SQL Server instance, but basically gives you a cut down version of the full SQL Server, enabling you to use more of its features.
Both of these are free.
TSQL is a language specification, not an actual database.
If you're talking about MS SQL Server, it is possible to bundle and install an instance of SQL Server Express, if you want to distribute a database with your app. There's some documentation on it over on MSDN, specifically, Embedding SQL Server Express into Custom Applications.
You might also want to check out VistaDB. It is syntactically compatible (although not perfectly) with sql server. All managed code. But it is not free.
SQL Server Compact Edition does not support stored procs, fyi. But is a single file deployment plus your data file.
SQLite is extremely fast and lightweight. Deployment is single file plus data file. But it has some syntactic limitations and has limitations to its dotnet integration (although I am pretty sure there IS a ado.net provider for it.)
I support an application built on sql express edition and it is a PAIN. It has a lot of install failures. (Probably about 10k installs over the last 3 years.) But if you need to power, hot backup, full sp and function support, connection pooling, etc it will work for you.
Never used mysql so I can't comment.
Seth