DOTNET and Mono by default only support database connections to the Microsoft SQL Server through System.Data.SqlClient module. To make a connection to the MySQL server you need a connector module from MySQL.
Proceed with the following steps to obtain and install the MySQL .NET Connector:
1. Downloading MySQL .NET Connector
Either from MySQL (requires registration):
http://www.mysql.com/downloads/mirror.php?id=399565
or directly from one of the mirros:
ftp://ftp.gwdg.de/pub/misc/mysql/Downloads/Connector-Net/mysql-connector-net-6.3.6-noinstall.zip
3. Unzip the content into a directory
~> md connector ~> cd connector ~/connector> unzip ../mysql-connector-net-6.3.6-noinstall.zip ~/connector> ls CHANGES COPYING MySql.Data.chm README Release Notes.txt v2 v4
4. Change names of assemblies to proper names
~/connector> cd v2 ~/connector/v2/ mv mysql.data.cf.dll MySql.Data.Cf.dll ~/connector/v2> mv mysql.data.dll MySql.Data.dll ~/connector/v2> mv mysql.data.entity.dll MySql.Data.Entity.dll ~/connector/v2> mv mysql.visualstudio.dll MySql.VisualStudio.dll ~/connector/v2> mv mysql.web.dll MySql.Web.dll ~/connector/v2> cd ../v4 ~/connector/v4> mv mysql.data.dll MySql.Data.dll ~/connector/v4> mv mysql.data.entity.dll MySql.Data.Entity.dll ~/connector/v4> mv mysql.visualstudio.dll MySql.VisualStudio.dll ~/connector/v4> mv mysql.web.dll MySql.Web.dll
5. Copy assemblies into library directory of your mono installation
~/connector/v4> su /home/user/connector/v4 # cp MySql.* /usr/lib/mono/4.0/. /home/user/connector/v4 # cd ../v2 /home/user/connector/v2 # cp MySql.* /usr/lib/mono/2.0/.
6. Register the installed assemblies in the global assembly cache
~ # cd /usr/lib/mono/4.0 /usr/lib/mono/4.0 # gacutil -i MySql.Data.dll Installed MySql.Data.dll into the gac (/usr/lib/mono/gac) /usr/lib/mono/4.0 # gacutil -i MySql.Data.Entity.dll Installed MySql.Data.Entity.dll into the gac (/usr/lib/mono/gac) /usr/lib/mono/4.0 # gacutil -i MySql.VisualStudio.dll Installed MySql.VisualStudio.dll into the gac (/usr/lib/mono/gac) /usr/lib/mono/4.0 # gacutil -i MySql.Web.dll Installed MySql.Web.dll into the gac (/usr/lib/mono/gac) /usr/lib/mono/4.0 # cd ../2.0 /usr/lib/mono/2.0 # gacutil -i MySql.Data.Cf.dll Installed MySql.Data.Cf.dll into the gac (/usr/lib/mono/gac) /usr/lib/mono/2.0 # gacutil -i MySql.Data.dll Installed MySql.Data.dll into the gac (/usr/lib/mono/gac) /usr/lib/mono/2.0 # gacutil -i MySql.Data.Entity.dll Installed MySql.Data.Entity.dll into the gac (/usr/lib/mono/gac) /usr/lib/mono/2.0 # gacutil -i MySql.VisualStudio.dll Installed MySql.VisualStudio.dll into the gac (/usr/lib/mono/gac) /usr/lib/mono/2.0 # gacutil -i MySql.Web.dll Installed MySql.Web.dll into the gac (/usr/lib/mono/gac)
Note: For steps 4 (renaming) and 5 (copying), I don’t really understand why these steps are necessary, but on my OpenSuSE 11.3 machine it did only work out that way. Any suggestions to improve this procedure are welcome.
Further reading:

I don’t really understand why these steps are necessary, but on my OpenSuSE 11.3 machine it did only work out that way.
Linux is case sensitive.
Correct, however, I think it is fair to expect that .NET with an origin from a non-case-sensitive environment would not get picky on this in a case-sensitive host.