Run the vocal signal through a compressor. This process will be different with every mixing setup. If using a computer to mix the vocals, you might use a software compressor. If using a mixing board to mix the vocals, you might use a hardware compressor. Regardless of the compressor you are using, the basic controls will remain the same.
Set the threshold level of the compressor so that it is right above the level of the quiet vocals. When the vocal level goes above the threshold, the compressor will turn on. This will cause the louder vocals to be compressed so they are kept closer to the volume level of the quiet vocals.
Choose a compression ratio based on how much you want to compress the vocals. A low ratio of 2-to-1 will allow the vocal level to increase 1 decibel for every 2 decibels the vocal level goes past the threshold. A high ratio of 10-to-1 will only allow the vocal level to increase 1 decibel for every 10 decibels the vocal level goes past the threshold. Choose a low ratio for less vocal compression or a high ratio for more vocal compression.
Select a fast attack setting if you want to the compressor to turn on quickly after the threshold is crossed or select a slow attack setting if you want the compressor to turn on slightly after the volume of the vocal has crossed the threshold.
Select a fast release setting if you want the compressor to turn off quickly once the volume of the vocal has fallen below the threshold or select a slow release setting if you want the compressor to turn off slowly once the threshold has been crossed.
Adjust the output gain of the compressor according to how much the vocal is being compressed. If the vocal is compressed by 10 decibels during the loudest vocals, then set the output gain to 10 decibels. This will make up for any gain lost, causing the volume of the quiet vocals to increase while keeping the volume of the loud vocals at relatively the same volume. This will help balance all the vocals at close to the same level.