How do I show that I am detail oriented on my resume?

Some people focus on the big-picture, whereas others are more analytical and detail-oriented.  If you are the latter, and those skills are requirements for the next job, there is specific language that will better convey to the hiring manager that you pay attention to organization and accuracy.  

For starters, always proofread your resume for grammar and spelling, multiple times, so that the recruiter will read an edited, properly-written resume.  Many positions, such as bank tellers; cashiers; anyone who is involved with accounting or legal assignments will have many clear examples of being detail-oriented.   However all professions require some level of attention to detail.  Proper descriptions of specific examples will offer strong evidence of your ability to be accurate and analytical.  For example:

“Consistently delivered thorough and accurate projects before or by the deadline” 

“Analyzed weekly sales numbers in order to provide management with profit/loss results.” 

“Carefully reviewed and edited documents prior to publishing, with no errors.”  

“Negotiated complex contracts with investors ensuring that all information was properly written.”

Being detail-oriented is more of a mental exercise as opposed to a specific skill.  So using the exact words, “detail-oriented”, is not necessary.  However, using action verbs and showing results in each example, will give the hiring manager a better understanding of your ability to think analytically, proofread or review your activities, and demonstrate that you are sufficiently organized and thorough to handle detail-intensive assignments.   Accuracy is very important in most jobs, so finding ways to include that information indirectly on the resume will appeal to the hiring executive.