My English is far from perfect. However, to make progress professionally in this English-speaking environment, it is a must to improve my English along the way. What I try to do is to improve my English on the job, one way or another.
I work in an environment where there are a number of Chinese colleagues, with whom I collaborate very closely. A blessing or not, we speak Chinese among ourselves. Of course, there are also "foreign" coworkers, including Americans in our group, and I do speak English with them. But such routine, brief communications help very little with my English.
One thing I do is to choose one colleague, who is a native speaker and is friendly, and to make it a habit to talk with him broadly during the breaks. In time, the topics have covered a wide spectrum of life. For example, he may tell me about his home improvement projects, which he enjoys doing a lot. On the other hand, I may choose some news items I saw on TV and discuss with him. Every time, I try to spend some time thinking about what I want to say and how I am going to say it before hand, so that I can minimize the number of grammar errors. Quite a few grammar rules tend to come to me as an after-thought, after the mistakes have already been made, which is quite annoying. By preparing, I make fewer such mistakes.
Another thing I do is to practice a number of times when I need to make a presentation. I would write down a few key sentences for each slide I have. Then I would practice giving the presentation, trying to keep it within the time limit, eliminate grammar errors, and make the transition from one point to the next as smooth as possible. And I would remind myself to speak up and be enthusiastic - I tend to speak softly. After practicing, I generally felt more confident. I would also be able to pay more attention to my audience and communicate with them more effectively.
Also, I try to keep a dictionary at hand so that I can look up a word whenever necessary. Wiktionary is a great resource that I use frequently. The only complaint I have is that Wiktionary does not have enough examples to illustrate the usages.
Finally, whenever I need to write something up, I also try to rewrite a few times before finalizing it, similar to what tcmquack wrote on this point. And "one sentence at a time" by huashe is indeed very good advice.
In summary, I think there are ways to improve our English on the job. I am happy to see that the few things I do seem to be effective. I'd love to share them with you, hear your comments, and see what you have to share. Thanks!
PS: If you see any errors in here, PLEASE point them out. Thank you very much!
PS: Several errors have been pointed out by the careful readers in the Workplace Forum. I have corrected the ones I know. I'm double-checking a few other points now. I'll update them as soon as possible.