Fleas can definately be spread through contact with other animals who have them.
Also, if your animal brings fleas into the house, and you don't regularly vacuum or wash carpets and beddings, (especially where the animal sleeps etc.), it is easier for them to reproduce as the eggs remain in these hidden locations and multiply the problem.
A flea doesn't care how healthy or clean an animal is when it comes to feeding. I regularly see animals who are of excellent health who have problems with fleas. Animals who don't use flea products can indeed have no problems with fleas...but usually that's luck and maybe even location.
My dog is in excellent health (other than an eye and petella problem which have no relation in terms of flea problems) and I found a flea on him before he was put on medication.
Fleas can still enter your house and live on your animals whether they go outdoors or not. Before I got my dog, I had two strictly indoor cats. One day, we found a flea on our cat and we couldn't figure out how it ended up on her. It turns out that my boyfriend had a family of racoons in his chimney and he may have brought them over to my house on his socks. Or...one may have jumped on one of us in the backyard and came in, which is a little more believable.
There are products available that will nip flea problems in the butt. Two that I have experience with are Revolution and Advantage Multi. They both work very well and protect your dog against heartworm as well (something that every dog should have protection against).
I would recommend speaking with your vet and having your dog in for an exam as there are specific doses depending on your animal's weight.
Furthermore, any form of heartworm medication should NOT be taken unless you have a negative heartworm test prior to usage as it can be dangerous to your dog's health.
I know you were only asking about fleas, but I thought I would mention these two products as they are essentially a two-in-one product (they also cover other internal parasites etc.) and are very important for your dog's health. This is assuming that you don't have him/her on any already.
If you must only use flea medication(although I don't recommend it), than I would suggest plain advantage.
Your vet can fill you in on everything about the product (if he/she uses it) or tell you about other ones they may use. Good luck and sorry for the long post.