The main rule in science writing is to ensure your prose is clear and concise so your audience understands the points you are trying to make. When I write, I generally don't worry about style and grammar until I've already had some read-throughs (by myself or a peer) where I edited for storyline, logic and flow.
Once you are ready to worry about style, go through each paragraph and check to make sure you are varying sentence length.
And easy way to check if your grammar is correct is to get someone to read your paper and highlight any sentences that they had to read twice or that slowed them down. There's a good chance that you can improve those sentences by editing the grammar.
I highly recommend "Writing Science in Plain English" by Anne E. Greene. You might even want to splurge on the <$20 paperback to have beside you when you do your style and grammar run-throughs. There are lots of easy-to-understand rules and great examples.
This site includes three detailed lessons on effective science writing: 1) Using subjects and actions, 2) Cohesion/Emphasis, and 3) Simplicity. I recommend reading through the second and third lessons. https://cgi.duke.edu/web/sciwriting/index.php
This site provides useful tips on sentence structure, verb usage, tense, mechanics, and punctuation. http://www.nature.com/scitable/topicpage/effective-writing-13815989
Here is a list of words to avoid in order to make your writing concise, clear and efficient. Words to avoid when writing