Living in fear of getting sick is silly because eventually you will get sick. You may be visiting someone's house and they will offer you fresh juice -- maybe their hygiene is not equivalent to yours, but you will not necessarily know that and you would be rude to turn down the offer (depending). So maybe you get sick. Big deal. A little diarrhea never killed anyone (well, actually it kills infants worldwide at a high rate, but you certainly wont die!).
Take normal precautions. Water is the main agent for parasitic infection. Drink purified water whenever possible. But some foods here are tricky, particularly pork, so be sure that the pork you eat is fresh. When you buy it, smell it.
Also beware the beso de ciguatera! Ciguatera is form of food poisoning carried mainly, if I remember correctly, by snapper and a couple other types of fish that feed around coral reefs. They digest a particular sort of bacteria and thus transfer the poisonous reaction to the next guy up the food chain -- you. You can read up on symptoms and remedies on the net.
A few home remedies for parasitic infections: if you have giardia, which is a common parasite, you can take Flagyl (metronidazole) to kill it. Some infections however do not respond so well and require a medicinal cocktail. In the meantime, to flush your system out, you can try te de sen, which is a purgative tea that also relieves constipation. You can also put two or three carrots and 2 or 3 cloves of garlic in a juicer, drink that down. Potent, a little "hot" on the stomach for the first five minutes, but once your stomach calms down, you will find that the parasites will stop bothering you. Dont know why, but it has worked on more than one occasion.