You may find these two links from our always useful reference section helpful:
Piggy body quirks (to help you learn what is normal and what not):
http://www.theguineapigforum.co.uk/showthread.php?t=58854
Early signs of illness:
http://www.theguineapigforum.co.uk/showthread.php?t=36332
Please weigh your piggies weekly; it is a good way to monitor their health. Guinea pigs are prey animals and are very good at hiding problems until it is rather late.
http://www.guinealynx.info/weigh.html
It would be good to have some kind of probiotic like avipro plus or biolapsis at home in case of a sudden illness/antibiotics. Some recovery powder (Critical care) is also useful to have at home, but in a pinch, mushed up pellets will do the trick if your piggy goes off food. You can google those products and get them over the internet.
Hopefully, your piggies will live a happy, healthy life if you take care to get them from a good place, like a reputable rescue that quarantines all incoming piggies and rehomes only healthy ones of a good weight. A good, diet and decent housing will also help to minimise many problems.
Make sure that you look for a good exotics vet or a piggy savvy general vet; ask a local rescue who they use or can recommend.
As to the most frequent problems:
Mites and fungal problems can make an appearance. There is no flea specific to guinea pigs, but especially if you have your piggies outdoors, you need to be aware that flystrike can affect piggies, too, and that regular cleaning and disinfecting of the hutch is a must, especially during the warm season.
If you are looking after your piggies well and are giving them a weekly check over, you are bound to notice any parasitic/fungal problems pretty quickly, when they are much easier treat and won't get past nuisance level. Please see a vet and don't home treat just on spec; you can do much more harm than good!
http://www.guinealynx.info/parasites.html
Otherwise, guinea pigs are rather prone to respiratory tract infections (URI), as they are not good with big fluctuations in temperature, drafts, dampness and the extremes of temperature (heat as well as cold). Please stay off wood chippings and dusty hay as that can cause respiratory symptoms that look like URI. Provide alternative accommodation in winter/keep your piggies cool and in the shade during heat waves.
Not every sneeze already makes an URI, though! Crackly/rattly breathing, looking off and being off food, crusty eyes and nose are symptoms of URI.
Urinary tract infections (UTI), as well as bladder stones/sludge are more frequent than in other pets because of their rather more naturally alcaline urine and their closeness to the ground. Putting your piggies on a still cold damp lawn when they are not used to it and haven't got the possibility to go somewhere warm and dry at all times can cause UTI - spring and autumn are the times when it hits most often. Always have any bloody pees investigated.
Guinea pigs can't make their own vitamin C (unlike rabbits) so it is necessary to feed good quality pellets (rather than muesli) to prevent selective feeding. it is also advisable to include at least one veg high in vitamin C daily (a slice of pepper of any colour, a bit of broccoli (any part) or a sprig of fresh coriander/cilantro, parsley, dill, mint or basil. Please vary between these. Do not overfeed veg. Piggy guts are laid out of coping best with mainly hay (up to 80% of the daily intake) to keep them healthy and fit - and therefore the piggy healthy and fit!
And lastly: DO NOT FRET AND PANIC ALL THE TIME! It takes some time to learn what is normal and what not; pet keeping is a lifelong learning curve and you are not expected to be a super duper know-it-all parent right from the start, remember that and keep a sense of perspective!
You are however welcome to post any questions you may have on here; we don't mind if they sound silly - better that than the opposite!
Best of luck and make sure that you enjoy your piggies, most and foremost!