How can I install dot net on linux wine and cross over?

"Disclaimer: This answer contains information which might be outdated soon and I could forget to update it. Please consult the provided links for current informations.

As John and SjB pointed out are there two ways for this. But (and that's a big one) whatever way you choose, you'll have to stick with 3.0.

Wine
You can install up to 3.0 under WINE without any problems (at least according to the AppDB entry). All newer versions have currently bugs in their installers and will not work.

Mono
The free port of the .NET Framework is compatible to 3.5, you can even take applications and just run them under Linux, without the need to recompile them. Unfortunately, there are some classes and functions (f.e. the HasRows() Property of the ODBCDataReader) which aren't implemented by now, and may throw an exception. Additionally to it, the Forms-Interface will look a little strange and out of place within Linux."