The only thing you need to do in this meditation technique is just passively observe the thoughts without engaging them. If you get a thought, 'Oh, I have to finish this work by tomorrow' while meditating, just observe it. Don't engage the thought by replying in your mind, 'Oh yeah, lot of stuff to do'. If you get a thought, 'I have to pick up the mail after the meditation', just observe this thought, you are not in a pressure mode here, relax, you will remember what you need to do once you finish the meditation. You see, the only thing that you have to do is be an observer, a passive spectator, see the games and tricks the mind plays, observe how it brings up the past, or the future. The mind does a good job of bringing up past hurts or future worries. See the thoughts the mind brings about passively.
Now, thinking, 'I have to just observe my thoughts, I have to just observe my thoughts' is NOT observing, but participating with the thoughts. So how do you get around this?
Before beginning the meditation, make an intention to just observe the thoughts and not get caught up in the thoughts that surface during observation. You don't have to silence the thoughts. Let them go on, but don't engage them either. Be a passive audience to the thoughts. It takes some practice, but with time, you will begin to not engage the thoughts and start to enjoy the meditation and the silence it brings about.
I personally have had quite a few meditations where the thoughts gradually died down without any effort on my part as the meditation progressed and the ensuing silence (or very few thoughts) was beautiful.
Here's a great article that elucidates this method.
Also, here's a post I wrote earlier on how the meditation practice unfolds.