There are a few things you need to do;

1. Download Connector-ODBC 5.1.6 and install it.

2. Download ODBC .NET Data Provider and install it.


After you finish that you need to setup the reference to it in your Project.
  1. Click "Add Reference"
  2. Go to the ".NET" Tab
  3. Locate and Select "Microsoft.Data.Odbc"
  4. Click "Ok"


You have officially got ODBC setup on your Computer and Project!



Here is a simple MySQL connection using the new ODBC Driver 5.1;

Code:
OdbcConnection Con;

try
{
	Con = new OdbcConnection(@"Driver={MySQL ODBC 5.1 Driver};Server=[IP];Port=[PORT];User=[USERNAME];Password=[PASSWORD];Database=[DATABASE];Option=3");
	Con.Open();
	
	MessageBox.Show("Connected.");
}
catch (OdbcException ex)
{
	MessageBox.Show(ex.Message);
}
finally
{
	Con.Close();
}
-Replace everything in RED with your MySQL Data-


The reason I made this little guide is because I spent 3 hours trying to do this, the reason being is that every guide was either outdated, incomplete, or just wrong.

If you have any issues with connection please feel free to reply.