To use a photo of a gray card to adjust white balance you need to adjust white balance (color temperature along the blue←→amber axis and tint along the perpendicular magenta←→green axis) until the values of the red, green and blue components of the gray card are all the same. When you hover the cursor over the gray part of the photo the values should be something like (128, 128, 128). Pure green, for instance, would be (0, 255, 0), pure red would be (255, 0, 0), and pure blue would be (0, 0, 255).

When we use a "color picker", the program tends to average the three values for the R, G, and B components and set all three to that value. Sometimes the automated routine will take other factors into account as well and bias the results based on them. That's why we can get really wacky colors if we click on an area that is totally blown out in all three channels.

To use a photo of a gray card to adjust exposure when post processing photos you just need to change the brightness of the image until the area of the gray card has a value of 128 on the 0 to 255 luminance scale.

When you have properly adjusted both white balance and exposure, you should wind up with an RGB value of (128, 128, 128) for the area of the image with the gray card.

Keep in mind that using only an 18% gray card to adjust exposure does nothing to set the brightest highlights at or just below 255 and the darkest shadows at or just above 0. It only sets an 18% gray card to 128/255. To set blacks and whites you need to use a black and white card and adjust using the shadows and highlights adjustments (or the ends of the "curves adjustments) after setting the mid-tones using the gray card.