It depends on the worm...but, for example, with hookworms (if I'm recalling correctly) the eggs are ingested; they hatch and live in the intestine for a few weeks; burrow through the intestinal lining, into the bloodstream and into the lungs for a while; then get coughed up and swallowed back to the intestine where they produce eggs that get pooped out... It can take a number of weeks for the whole cycle. And, since worms can be at different stages of the life cycle depending on when the eggs were ingested, you have to do two treatments for them about 3 weeks apart.
One thing to worry about with hookworms is anemia because there is a certain amount of intestinal bleeding that occurs with an infestation. But typically, the dog would have to have a very heavy infestation for a long time for anemia to occur.
Tape worms sometimes cause weight loss because a heavy infestation of worms can suck up all the nutrients before they get out of the dog's intestines into the blood. But again, it usually takes a long while before the effects are noticeable.
If you think about it, all wild animals carry a burden of internal parasites. As long as they're in fairly good health otherwise, they do okay.
So... TMI?