How can I make a single instance form (not application)?

You need to prevent the form from closing. If you don't, the form will be disposed and becomes unusable. You can do this by implementing the FormClosing event:

    protected override void OnFormClosing(FormClosingEventArgs e) {
        if (e.CloseReason == CloseReason.UserClosing) {
            this.Hide();
            e.Cancel = true;
        }
    }

To make it a singleton, just keep track of the life time of the form in your main form class:

    frmOptions options;

    private void btnShowOptions_Click(object sender, EventArgs e) {
        if (options == null) {
            options = new frmOptions();
            // To make absolutely sure:
            options.FormClosed += (o, ea) => options = null;
        }
        else {
            options.WindowState = FormWindowState.Normal;
        }
        options.Show();
    }

Well, the simplest way is to have a static field which stores a reference to the single instance or null, and then a method to retrieve it or create a new one.

Note that this isn't the same as making it a singleton - because I assume if the form is closed, you'd want to create a new instance next time. (The alternative - hiding it and reusing it - is shown in STO's answer.) You may want something like this:

public class OptionsDialog : Form
{
    private static OptionsDialog openForm = null;

    // No need for locking - you'll be doing all this on the UI thread...
    public static OptionsDialog GetInstance() 
    {
        if (openForm == null)
        {
            openForm = new OptionsDialog();
            openForm.FormClosed += delegate { openForm = null; };
        }
        return openForm;
    }
}

You may want to make the method perform the "bring it to the front" steps as well, of course.