If you are looking for just how to make the SQL statement work, you should try this:
_strQuery = "SELECT * FROM tblBibloteka WHERE Emri Like '" + txtKerko.Text + "%'";
The percent sign is a wildcard character, which means that if you are looking for data that STARTS with the letter, you want the wildcard to only appear AFTER that letter.
However, depending upon how your program works and how much data your database has, I'm guessing that it might function quicker and cleaner if you grab everything and instead of hitting the database each time you want to filter, you can just filter the data you already have. If you've connected your data to the DataGrid using a DataTable, you can just set the DataTable's .DefaultView.RowFilter property
You can use the .RowFilter much like the WHERE portion of an SQL statement. For example you could set it to
"Emri Like'" + txtKerko.Text + "%'"
And if you're actually wondering about how to connect to MySQL...you can check out http://www.connectionstrings.com/mysql
] for info on what the connection string needs to be set to. You can also search on google
] for articles on how to connect. Some of the ones listed there are even CodeProject articles.
Hope this helps.