Simple temperature converter
The main change is separation of logic and User Interface. Firstly the calculation methods should ideally not reside in UI methods like event handlers.

Secondly the calculations should really be in it's own class, (but this application is just small enough that it is not ENTIRELY necessary).



in programming we hate Magic Numbers. If you can, move any numbers littered around your code and name them something useful. 

so:

As 9/5 + 32 is equal to 1.8 (+32) and that number represents the scale difference, if we declare that at the top of our code like

double FAHRENEHEIT_SCALE_DIFFERENCE = 1.8;  
double FREEZING_POINT_OF_WATER = 32;


Depending on how much you have covered thus far you should then move the actual conversion to it's own method. 

(because if you come back to this code in 12-18months will you be able to remember what it does? What if it quadruples in size with more features?

So:

I would suggest something along the lines of

public double convertCelsiusToFahrenheit(double celsius)
{
  return celsius * FAHRENEHEIT_SCALE_DIFFERENCE + FREEZING_POINT_OF_WATER;
}


Next, 
you can tidy the button click.

private void btnConvert_Click(object sender, EventArgs e)
{
    double celsius = double.Parse(txtCelsius.Text);
    lblFahrenheit.Text = convertCelsiusToFahrenheit(celsius);
}




Finally the golden change is the separation of the logic from the interface.

Now that you have a simple method that is separate from the actual screen; you could move it, and all similar methods into it's own TemperatureConverter class, or something similar.