Diving both in length and depth requires practice and being completely familiar with water. You have to learn to be confident that your oxygen will be sufficient for long enough. Practice: hold your breathe on the surface with a timer and then test that you can hold it AS long under water. Individual differences matter: the bigger lungs the better.
Different techniques can be used with diving: without fins its better to use breaststroke kicks with slightly modified hand stroke, with fins its better to just kick the free style kicks with maximum force, hands being straight in front and head pressed between them (gliding position). Also so called dolphin kick where the lower back and waste are empowering the legs is very powerful.
Diving to depths, it’s important to manage the water pressure: squeeze your nose closed with your fingers and blow into your nose gently, so that your ears will pop open. The deeper you dive, the more often you have to repeat the same process. If you are experienced, you can easily dive deeper than 10meters without any equipment.