You don't need much equipment to look after a guinea pig. Nail clippers (the ones made for human use), a basin for bathing, a hair dryer with a cool setting, a fluffy towel, some guinea pig shampoo and a guinea pig brush - that's about it.
Some owners ignore the branded guinea pig shampoos and use a gentle variety made for human heads. Always check the ingredients, though - harsh detergents will not teat your GP's skin very kindly, and can cause upset stomachs after being ingested during grooming. As baths for guinea pigs are infrequent, paying for a small bottle of proper guinea pig shampoo isn't going to break the bank, and it will last you a long time.
Looking good - a freshly groomed Peruvian Guinea Pig
Guinea pigs will get a build-up of grease on their rumps over time, residue from their grease glands (they apply a sticky substance to objects to mark their territory). This can be removed with mild washing up liquid or a grease dissolver fit for human skin.