Writing a concise, easy-to-follow CV is an important skill, and is essential for soliciting recommendation letters, applying to graduate schools and REUs, and eventually for applying for job. Some things to keep in mind:
Organization is key. Clearly indicate what you are listing in each section of your CV, in a standard font.
For many purposes, recruitment committees may need to know your citizenship/residency status. Mark it clearly in your personal details, which should be the first section of your CV. Other personal details, such as phone number, address, or birthday are better not listed.
Keep each section short; only in rare circumstances should the CV of a university student be longer than two pages.
You may need to tailor your CV to the programs to which you are applying, by highlighting relevant skills/coursework.
It is appropriate to list awards/achievements, though recent awards (i.e. ones from your time as a university student) will carry more weight than ones from elementary and secondary school.
It is appropriate to list outreach activities (such as tutoring, community service, etc.), and this can be especially helpful for graduate programs.
It is appropriate to have a short section at the end of the CV listing activities that are beyond the scope of the position to which you are applying.
Ask your peers for examples!