The textbook definition of mindfulness is "a mental state achieved by focusing one's awareness on the present moment, while calmly acknowledging and accepting one's feelings, thoughts, and bodily sensations, used as a therapeutic technique.". If you're an anxious person, almost all of what is stated above seems impossible. Constant, racing thoughts makes it hard to remain focused, as well as achieve a sense of peace of mind, or quietness of mind. It takes practice, and it's hard.
Mindfulness isn't something we achieve over night. You have to take it day by day. Maybe practice three minutes for one day, then try to take more time as you progress.
Being mindful isn't something you have to go out of your way to do. Practice it while brushing your teeth in the morning, or cooking breakfast, or just when you finally get to sit down after a long day at work.
Mindfulness has been shown to approve feelings of anxiety and stress, and just because you feel bogged down by these feelings, doesn't mean you can't be a "mindful person".
These practices can then be taken and implemented in our every day lives. If you ask me, we could all take the time to practice being a bit more mindful of ourselves, as well as others.