For the most part, a healthy, thriving cavy will do most of the work in keeping themselves clean, leaving just a couple grooming tasks for you.
In addition, some guinea pigs will naturally require more time and attention -- Silkies (pictured below) have gorgeous manes which can require brushing, removing tangles, and even trim hair. Male guineas will also need assistance in cleaning their grease glands (which help mark their scent).
Sheltie guinea pig -- an example of a long-haired piggy needing more time and attention.
Above, a guinea pig grooms itself by standing on its hind legs and will brush its fur with its front paws.
BATHING: Do not let the thousands of pictures of guineas in bathtubs on Instagram to fool you -- actually bathing a guinea pig in a bathtub should not occur regularly. They self-clean by secreting a milky white liquid from their eyes, then use their hands to gather the liquid and disperse it throughout their fur. A water-and-soap bath should be used when they have excrement in their fur (some pigs are fond of rolling in their potty-time products), or when it is clear they have enough mess in their fur to warrant a bath. Use warm water and a guinea-safe soap. DO NOT ALLOW YOUR PIGS TO SWIM. An inch or so of water is plenty. DO NOT leave them unattended. After, use a warm blow dryer and fluffy towel to dry them (keep the back of your hand in the stream of hair so you know it's not too hot). Research more if you must give your guinea a bath!
NAILS: You will need to trim your pig's nails about once a month. Take extra care to avoid the quick, which is the blood vessel supplying the nail. Trimming the nails is not painful to your pig (when done correctly), but most do not view it as a relaxing spa treatment, either. Check out GuineaLynx's page (http://www.guinealynx.info/nails.html) for in-depth information as well as step-by-step instructions from experienced guinea owners!