Well I've been practicing meditation for about a year now and here's what I can tell you.
Stop being so hard on yourself!
Everyone's always like... 'my mind races, i can't concentrate blah blah' for some reason I think Americans have this picture of perfect focus lasting for hours for these "special" people who can meditate. Before you start your session toss all that bs out the window. Everyone who meditates will tell you it's a pain. All of our brains get active when we try to quiet them. But through meditation we can realize that the working of our brain are just that... all in our mind and not anymore real than any other thought we have, whether it's fear or anxiety.
Now there has been a lot of great stuff put down in here all ow me to just give you my rundown for starting meditation. Sounds like you have a cozy spot to do it that's good, make sure you've got cushions (zafu/zabuton if you got it, some firm pillows if you don't). You want to sit so that just your rear is on the edge of the pillow allowing your legs to tilt down slightly. This allows you to maintain curvature in your spine. We're taught here to bring our hands together, placing the left fingers over the right in a cup with the thumbs touching lightly (think of holding a piece of paper between them) in the middle, centered on your belly button. Now before you start remember that you will not be perfect, that no one but enlightened zen masters can achieve such focus. That's not to say it's unattainable, just to say that for most of us we're looking for that 5-10s of enlightenment. Also place in your mind the thought of how you will treat yourself when you sit. Try to envision before you start how you would treat a very small child that is walking down the sidewalk with you, and tries to cross the street without looking. They don't know any better so gently help them back onto the sidewalk. Use this for yourself when your mind wanders.
Now for the actual sit.
I generally start with a focus on the breathe.
Specifically the space just at the tip of my nose where I can feel the in and out breathe. Tying into your breathe is the easiest way to feel 'right now' since it's going to happen no matter what you have to say about it unless you're dead...
Counting 1 on the in breathe and 2 on the out, up to 10. I try this a few times until I feel I've sufficiently focused on my breathe.
Then from there you can approach it several different ways.
In the form of Zen Sword I study we learn mind training where we see ourselves practicing kata in the 1st person as if we were doing it in the room. Trying it faster and clearer each time we repeat it in our mind. If you're a martial artist I would think you can adopt this. For me and most here it has given a great means of attaining more clear mind in meditation. That said if you want something else often a mantra helps your mind to focus.
Such things as love, compassion, family, joy, empathy, a name of one of the boddhisattvas (Avalokiteshvara, Kwannon, Kwan Seum Bosal) can all be your constant focus. They will of course get overrun by your mind but that will just help to show you as you slowly bring yourself back to focus like you would that child, that you can retrain your mind and you can gain a bit of clarity.
Also don't strain yourself at first. For the first month I started meditation I just did 5minutes in my bed before I slept. Might not have been the most useful application but it still beat doin nothing. Hope this helps.