Loudness, like pitch, is a perceptual attribute. In acoustics, loudness is measured in intensity or sound pressure level. Physiologically, loudness corresponds to subglottal pressure. Changes in loudness are proportional to changes in subglottal pressure.
One way to increase subglottal pressure is with respiratory activity. Specifically,increase in expiratory muscle force. If you start with a larger lung volume by inhaling more air, you get larger relaxation pressures and you don't have to work so hard with the expiratory muscles.
A second way to increase subglottal pressure is with laryngeal activity. You can increase adductory muscle force and close the glottis more tightly. Trained singers can do this. For loudness, the vocalis muscle is very important, especially at high frequencies. If you are a nonsinger, you have to rely on other muscle activity. The lateral cricoarytenoid muscle and interarytenoid muscles (both transverse and oblique) can hold the arytenoids more tightly in the back. These muscles are not used as often as the vocalis to make glottal adjustments.