How to use code by direct shortcut key on button

First off, CTRL+S shouldn't be "Search" - the Windows convention for CTRL+S is "Save" and swapping that around is a bad idea - it confuses users. The convention for "Search" is CTRL+F or F3

The simplest way to add a shortcut is to use the designer: Highlight your button and look at the Properties pane. Select the Text property, and add an ampersand in front of the letter you want to use: "&Save" will set ALT+S as the shortcut.
Unfortunately this only works for ALT+key combinations.

For CTRL+key you need to do two things:
1) Set the Form.KeyPreview property to true.
2) Override ProcessCmdKey:

protected override bool ProcessCmdKey(ref Message msg, Keys keyData)
    {
    KeyEventArgs e = new KeyEventArgs(keyData);
    if (e.Control && e.KeyCode == Keys.F)
        {
        DoSearch();  // Your method here.
        return true; // Handled - prevent it being passed down the chain as well.
        }
    return base.ProcessCmdKey(ref msg, keyData);
    }