That’s a big question. How much of a Chinese environment are you in? Do you get daily conversational practice?
I read somewhere that it takes at least 20 different exposures to a word in different easily understandable contexts to get a grasp on a word. For me, what made the biggest difference is hearing the ChinesePod dialogues over and over. Within a level, the same words are repeated many times in different contexts.
As I started being able to remember the tones on the less familiar words, actually using them in conversation was the key. It was a slow process. Even in a Chinese environment, I’d say it typically took me a month to get a word in passive vocabulary, then another month to move it into active vocabulary.
But I was 29 years old when I started. My younger classmates (2 in particular) seemed to be able to pick words up almost instantly.
Incidentally, I’m sure some westerners have learned some Chinese from reading the news, but I have yet to meet even one of them. I think our Japanese classmates did OK with it, but the rest of us were just too exasperated to learn anything. Even when we did manage to understand something, we felt like we had just spent an hour with Sir Humphrey: