There's Buddhist theory, and there's Buddhist meditation. Like any religion, there are countless interpretations of Buddhism, but most put the practice of meditation before theory. (Buddhism is sort of like an anti-religion that way. Instead of faith, Buddhism at its core is based on the experiential.) Really, most of the theory is a way of talking about what you come to understand if you meditate a lot, so it's pointless really to talk about it without meditating. To answer your question, being in the moment takes practice, and that practice is meditation. Through a friend, I was lucky to find Vipassana meditation. Vipassana focuses very specifically on body sensation, and the meditation begins with paying attention to the breath. As you do it, you begin to experience your own thoughts (for example) as just another sensation. Thoughts happen. We usually identify ourselves with our thoughts, but they happen with or without us. They have a sensation you can observe. They are part of the moment, but not its totality. Same with anxiety, since we're on the topic. Anxiety is just a word. What's the sensation? My chest feels hot, my lungs feel tight, my heart is racing...it's just part of the moment. So, rather than BEING anxious, it's more like, 'Anxiety is happening. Observe the sensation.'
Long post, sorry. That answer your question?