It seriously just takes more, and more consistent -- it took me something like a decade before I was what I'd consider somewhat capable of some very basic meditative tricks, mostly related to breath control and muscle relaxation -- effort. I say that coming from that exact position of constant-thought and occasional insomnia.
It took me a good three months before I could reach the "no thought" point with only 10 minutes or so of work. Of course the reason I was doing this in the first place was because I was being haunted by terrible nightmares which if I cleared my mind before I went to sleep didn't occur. Horrible nightmares if you fail are a good incentive to work hard at learning something quickly, but I don't wish them on anyone else ever. I think that being in band (where we do all sorts of breathing and breath control exercises) also helped me out a fair bit on that front too.
And as Frumple mentioned the first step to meditation is just paying attention to your breathing. If you have time just sit still, relax as much as possible, and just breathe (this is a good time to practice deep breaths as well, which are breaths were your stomach moves but your chest stays relatively still, which is the best way to breath 95% of the time). You can even think "breathe in, breathe out, breathe in, breathe out...", if you need to, it can be a big help while learning. The thing is that while you are thinking "in, out" you aren't thinking all of the other thoughts that you normally would be. That's why there is the whole "oommmmm" thing with meditation. If you can fill your mind with that one syllable, then that means you are only one syllable away from filling your mind with nothingness (you'll notice the meditation masters don't hum syllables often, they just sit quietly). I find that the other thing that helped me early on was that while I was thinking "in, out" if I ever felt tense I would just say out loud "relax", while breathing out, then go back to thinking "in, out". Then I would just keep doing the in, out, and relax over and over again until I was completely relaxed. After some practice you will need to say relax less and less times to let out all of your tension, and you will get better at focusing completely on your breathing while ignoring outside distractions. At that point you might consider moving to an ommm or similar syllable instead of "in, out", moving back to the "in, out, relax" pattern if you ever start to tense, before moving back to omm when you relax again. Eventually you will reach the point when you don't even need to ommm, you just sit there quietly. But don't get discouraged if it takes time to reach that point; for as Frumple pointed out, the process can take years or decades to learn, and even meditative masters still ommm from time to time.