What is the best way to proofread my resume?

Check it in several separate passes, each looking for one kind of problem, and use more than one method. A single quick read misses many errors because your brain fills in what you meant to write.

A reliable routine:

• Run a spell-checker set to the right English variety, and review each suggestion rather than accepting all.
• Read the whole resume aloud, slowly.
• Check facts: names, titles, dates, numbers and contact details against your records.
• Check consistency: date format, punctuation, capitalisation and tense.
• Look at the final PDF on screen and, if possible, printed.
• Ask one other person to read it.

Take a break between writing and proofreading; even a few hours helps you see the text with fresh eyes. Proofreading the final exported file matters most, because that is exactly what the employer will see.