Assuming that the ground speed of an airplane is the air speed plus or minus
The head or tail wind; how is the ground speed calculated when flying in a cross
Wind (either at a right angle to the wind or on a diagonal course)?

Use your E6B flight computer.

E6B - Wikipedia, the free encyclopedia

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To solve this problem with a flight computer, first the wheel is turned so the wind direction (C) is at the top of the wheel.
Then a pencil mark is made just above the hole, at a distance representing the wind speed (D) away from the hole.
After the mark is made, the wheel is turned so that the course (A) is now selected at the top of the wheel. The ruler then
is slid so that the pencil mark is aligned with the true airspeed (B) seen through the transparent part of the wheel.
The wind correction angle is determined by matching how far right or left the pencil mark is from the hole, to the wind
correction angle portion of the slide's grid. The true ground speed is determined by matching the center hole to the speed
portion of the grid.

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See video
E6B Flight Computer: Ground Speed and True Heading - YouTube