Set up a work area that's as out of the way as you can make it. Set aside ample time to do your work. Despite what many people believe, copy editing isn't easy. Copy editing requires attention to detail that can easily be disrupted by outside activity. Some copy editors get so accustomed to working in a chaotic environment that they have no trouble tuning out when they are reading, but unless you have been doing it for a while, copy editing under those conditions can cause you to overlook details. Ideally, find an office area where you can shut out the world while you work. If you work in an office without the luxury of your own quiet space, consider getting headphones to drown out the surrounding noise.
Try doing your copy editing in two or three rounds. On the first round, look for issues with language and structure. If you spot typos or spelling errors on the first read through, make a note of them but keep your focus on the structure of the piece. The second round of reading should be for mechanical errors and typos. Some editors do a final reading to ensure their work is thorough. Other copy editors add a reading from the standpoint of a general reader as opposed to a working professional. By breaking your work down this way, you stand a better chance of doing a thorough job.
Take advantage of software spellcheckers and grammar checkers built into your word processor, but never rely on them. A spellchecker and grammar checker can take some of the strain off your tired eyes and shave a little time off your work hours by catching or highlighting obvious errors, but because neither of these tools can understand context, relying on them completely will make a mess of your work. Use these tools only as a way to roughly gauge the shape of the manuscript. FileCleaner (see Resources) is one handy tool all editors might want to consider. It's a Word add-in that cleans up extra spaces, automatically fixes quotation marks and turns hyphens into em dashes, and many other time-saving functions for copy editors who do a lot of tedious work.