Practice, practice, practice.
I recommend practicing (to yourself, either in your head, or even better, out loud to a mirror) giving short technical "presentations".
There are two forms this can take. The first is to work, generally, on your ability to communicate technical topics. For this, find a short, but interesting, technical paragraph (from a book or a blog, etc.), related to a concept you know pretty well, and practice giving a two sentence summary "presentation". Try and figure out how you can convey the important stuff, as simply and cleanly as possible.
The second form is to also use this technique to prepare for something you might actually need to present in a work context. If you know you will be required to give an update tomorrow, spend a few minutes thinking of exactly what you want to say, and then practice giving that update. Run through a few iterations, changing the order you present things, improving precision, but reducing complexity, etc.
I'm a native English speaker (and work in English) and I still do this all the time. If I'm scheduled to meet with my boss, I'll practice a few important sentences I know I want to say. If I anticipate a few questions, I'll practice the answers.
The purpose of this exercise isn't to memorize specific sentences (as that really isn't useful for a conversation), but to get a good feel on how much information you can pack into a sentence, how to make sure the important parts aren't buried, how to make sure your thoughts are correctly conveyed.