To care about yourself is to care about the mind as well as the body. If you don't get sick, your body practically works in the background. You don't think about it, you don't notice the processes inside. It's a good thing we've evolved this way. Otherwise, we'd probably go crazy getting data about every one of thousands of processes from all the organs 24 hours a day.
We control almost nothing in the body. Everything happens automatically. But, when needed, you can almost enable perception, to some degree. Your body and its ability to feel the world is the best tool for awareness. Breathing is amazing, because it works automatically until the moment you think about it. Then suddenly you take control and you can slow it down and speed it up, or stop it altogether. For a while. Then the body starts to fight you and takes control again.
Consciousness is akin to a physical skill. You go to the gym to have a healthier body. You exercise conscious attention to have a healthier mind. But just like regular gym routine does not help if the rest of the time you are sitting incorrectly, eating nonsense junk food or not sleeping enough. A good attitude towards the body implies a lifestyle, a common system of values, the choices you make throughout the day. The same applies to your mind. Regular meditation is great, but if you do it to counteract the crazy days filled with "junk food for the mind", then something is wrong.
You can practice awareness at any time, for a few seconds. Standing in line? Turn your attention to the moment, notice all the voices, sounds, smells, sensations in the body, air movement, the way your clothes touch your skin. Just notice the world. Washing the dishes? Pay attention to the water temperature, how it touches the skin and what it feels like. Notice the contrast between the skin that's warmed up by the water and the neighboring area. Just notice the world. Reading this paragraph now? Notice the position you're in, how your fingers touch the phone or the keyboard, what it feels like right this moment. You can just give it a simple description in your head: cool metal of the phone, a little itchy behind the right ear, the shirt touches the chin, it's soft, outside the window a car driven by.
Just notice the world.