The first thing to do is add this to the using section if not there already:
To get the files from a folder, you can use:
string foundFiles = Directory.GetFiles(thePathVariable, theSearchBoxText + "*.*");
You have to change "thePathVariable" and "theSearchBoxText" to suite your needs.
By appending the wildcard string ("*.*") you're searching for every file with any extension that starts with the text written in your search box. You can play with the wildcards to achieve any other needs.
To display the results into a datagridview, we have to transfer the data from the string array to a datatable. This can be also achieved easily with LINQ, but seems you're not quite there, so:
DataTable s = new DataTable();
foreach (string aFile in foundFiles)
dataGridView1.DataSource = s;
And that's it, hope it helps.