A resume should be only 1 page long! This presents a meaningful challenge in conciseness. For me, personally, a good rule of thumb has been to tease rather than explain, and generally invite questions which the reader may want to ask during an interview (e.g., "I saw you said .... Tell me more about that!").
A resume is not just a shortened CV! Whereas a CV is essentially just a bulleted list, hirers in industry expect resumes to "tell a story." If you create a resume by just paring down your CV, the result will not be perceived as compelling by most folks outside academia. Rather, a fundamentally different approach is needed.
Time improving your resume is always well spent! This annoying piece of paper has a monumental impact on your career, the extent of which is frustratingly impossible to measure.
Exemplify! Give your best examples possible of going above and beyond. For example, don't just list your degree and GPA; rather, mention any distinctions you received, such as dean's list, scholarships, etc. I've found that a good rule of thumb is to adopt an attitude of narration: describe scenes which the reader can imagine. For example, don't only say that you took classes in some subject xyz; rather, mention if you wrote the class's lecture notes (sometimes, professors ask for volunteers to take notes in TeX and share), if you caught an error in one of the exercises or otherwise contributed to a textbook's errata, if you organized some group study-sessions with your classmates, etc.
Quantify! Instead of only saying "I taught calculus," mention how many students you had, how many sections, how many semesters, etc. Instead of only saying "I did research," mention how many collaborators you met with (and how often), how many papers you read during your literature search, etc. Give dollar amounts whenever possible (e.g., for fellowships); it'll make some hirers' eyes pop out of their head while they do an "awooga" noise. To be honest, I'm not sure I entirely understand why some hirers crave numbers, but whatever, I guess. It is an expectation that's in your best interest to meet.
Talk like caveman! Instead of saying "During this position I worked on [whatever]," just say "worked on [whatever]," (see, also, the next point). As with the above, I don't entirely understand why complete sentences are so hated by some hirers, but whatever. Maybe, people outside of academia are not used to reading essay-style writing?
Emphasize the impact, the "why!" You're always advised to use strong language on resumes. That's easy: instead of saying "worked on [whatever]," bust out that thesaurus and find an appropriate word that's more impactful, like "conducted," "invented," "formulated," "solved," "composed," "presented," as the case may be. However, I feel that this common advice is really just an overly superficial version of the superior advice that you should emphasize the impact of your work, rather than merely stating the content of your work. For example, in reference to an ML project, instead of saying "[did whatever whatever] to prevent memory overflow," it would be stronger to say something like "enabled support for neural networks with x% more parameters, leading to a y% increase in predictive accuracy, by [doing whatever whatever] to prevent memory overflow." That's too verbose but, hey, it's just an example.
Know your audience! This is easiest to achieve if you can have a conversation with someone from the company, either at a career fair, or simply an informational interview. Try to figure out what the group's priorities are, so that you can be sure to address those clearly on your resume.
Breadth is important, too! You never know what will pique the interest of the person reading your resume, begging some question to be asked in an interview. I try to remind myself I should have so many awesome things to talk about that I can't possibly afford to linger. Given the 1 page limit, it is certainly a challenge to balance breadth with the level of detail implied by the other items on this list, which brings us full circle to the first point: brevity. If done correctly, your resume should read like a mic drop, with nothing more needing to be said.