How to wait until button first click process completed?

If this is Windows Forms application, might as well just disable the button as soon as the event is fired and enable it when finished the processing.

Another technique is to have a boolean variable and change it's value. On subsequent click check it's value to determine if processing is going on. On completion of processing revert it to original value.

You wish to be more user friendly, consider doing the job in background, keep track if processing is going on and inform user accordingly.

At least user will be able to perform some other tasks.