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I used to worry about this when I was a grad student too. I'm now the lead writer in my scientific collaboration.

You can be comforted that most academic papers are very, very poorly written :)

A couple of things I've learned so far are:

• anyone can write a scientific paper. If written correctly, they have no personality, expression or artistic character. We just say what we need to say and then are done.
• terseness is key (in my field anyway). My advisor used to say that once you write your first draft, read through it again and see if you can't eliminate 1/3 of the words.
• Don't write the paper "in order." I always write my methods section first when I do my experiment or calculate, then generate result figures, then draft the results/discussion section. The introduction and conclusion should always be written last, and after the fact.
• Some students worry about volume. But if you are close to an experiment or result, you'll find you have a lot to say about it. Your advisor will look over your draft and help train you to know what elements of your setup are important to highlight.

If you want just a collection of "tips" for academic writing in general, I might recommend Style by Joseph Williams. His work applies probably more to essays than scientific papers, but I found his tips for writing very helpful when making my dense papers actually readable (e.g. put all the jargon at the end of the sentence, not the start, make the actor the subject of the sentence etc.). Be advised that most scientific papers are pretty darn unreadable and they certainly don't follow ANY of William's tips, but I include them in mine for that poor grad student trying to introduce themselves to my field.

When I was applying, I got this book by Donald Asher: Graduate Admissions Essays. There were examples in there, but also a lot of practical advice and tips on how to write a successful statement of purpose. I found it really helpful when I was applying and writing.

You can also ask your professors if they have examples of past students' essays to share; some colleges also keep examples on file, either at the departmental level or in some other office. For example, my college's office of study abroad kept old successful Fulbright and other fellowship applications on file, and my graduate school had successful NSF statements on file for us to peruse.