There are many questions and confusion about the reproductive cycles of dogs and cats, so I thought I'd give a quick lesson in canine and feline sex issues.
Dogs and cats reach sexual maturity at around 7-9 months old. At this time the sexual organs are fully formed and producing full amounts of hormones. Once this happens, they start to exhibit behaviors related to the gender and become fertile. Females are only fertile and receptive a few times per year, unlike humans.
The heat cycle in both species begins similarly. Initially there is a period lasting 7-10 days where the ovaries begin producing hormones and prepare to ovulate. In dogs, this is accompanied by vaginal bleeding similar to what happens in a human woman's menstrual cycle. Cats do not have noticeable bleeding, but begin to exhibit strange behaviors such as increased affection, presenting their tails and hind end, and strange vocalizations (what I often term "demon-possessed"). Cats are also what are called induced ovulators, meaning that even though they are reproductively "ready", they won't actually release their eggs until they have intercourse with a male.
A dog's fertile period begins once the bleeding stops. For the next 7-10 days they are ovulating and can become pregnant. An interesting tidbit is that because ovulation takes place over several days, dogs and cats can mate multiple times, with the potential for different males fertilizing the animal. It is therefore possible for siblings in a litter to have different fathers.
If the animal doesn't become pregnant, they will begin their reproductive cycle again. Dogs will cycle every 6-9 months, so usually a couple of times per year. Because cats are induced ovulators, once they start going into heat they will continuously cycle in and out until they mate. This can go on for months without end and can be very annoying to the cat's owners.
Pregnancy in dogs and cats lasts about 2 months, an average of 61-63 days. The size of the litter varies based on the species, breed, and size. Smaller dogs usually have smaller litters than larger ones, and first pregnancies tend to produce smaller litters than later ones. Most of the time delivery is routine and uncomplicated, with the animal cleaning the babies and stimulating them to breathe and move.
On the male side of the equation, here are a few interesting trivia facts that you probably never wanted to know. Dogs have tissue at the base of the penis called the blubous glandus. When the male becomes excited, this structure swells, forming a "knot". During intercourse with a female, this part of the penis is inside her vagina, causing them to "lock" together. This same structure can also become enlarged when the dog is extremely happy, and to some people can look like testicles, making them wonder if the dog was actually neutered. When the male and female are locked, the male will turn around to face away from the female, remaining inserted in her. This puts them back-to-back until he finishes inseminating her. And yes, his penis can bend that way to point directly behind him.
Intact male cats have barbs on the end of their penis that causes strong stimulation when he has intercourse with a female, causing her to ovulate. These barbs are dependent on testosterone, and when the male is neutered the barbs disppear.
Now it's up to you to figure out exactly when to use your new knowledge at cocktail parties.