Is that a real baby?

This question was asked in MetaFilter, and the top response references a Mental Floss article. This references the California Child Labor Law, which allows a (relative) newborn of 15 days old to be "employed in the entertainment industry".

More on the use of babies on film, from Mental Floss:

Some star-struck parents of prematurely born twins are able to cash in on their early-bird babies by allowing them to appear in TV shows or films as a newborn. Unless it's a reality medical series, most childbirth scenes in television and films are make-believe. Child labor laws vary from state to state, but in California, where the majority of those productions are made, a baby has to be at least 15 days old in order to get a work permit. Of course, most full-term babies have lost that "newborn" look after two weeks "“ their eyes are wide open, they've gained some weight, and their heads have begun to round out. So casting directors seek out "professional preemies" "“ babies born before their scheduled due date (twins preferred, in order to skirt around that 20-minutes-max camera time rule) but who are healthy enough to be brought to the studio. The law counts the actual date of birth, not the expected date, so, for example, a baby born after only seven months' gestation is still going to look tiny and fragile and appropriately "newborn" at the age of fifteen days. The law forbids smearing makeup on newborns, so cream cheese and jam are used to give them that authentic "fresh out of the uterus" look.

So that baby? Could be real! Just older than two weeks old, and covered in breakfast condiments.

A reporter from the Guardian investigated this.

You cannot use newborns because actors need to be a member of SAG, and you can only become a member if you're 15 days old.

“Our initial intention with Knocked Up was to film a live birth, but we found out we couldn’t because the baby, by virtue of not being born yet, couldn’t be a member of SAG. So we created a fake lower body of a woman with a head that came out to simulate crowning. There are a lot of regulations.”

Babies can also only be used for a short time:

Per usual, my questions are more macabre than their answers. Infant actors are well-protected; they can only work four hours per day; they can only shoot for 20 minutes of those hours.

“So you have four infants, approximately the same age, same hair color, look enough alike that they can double each other,” said Chris Riddle, an assistant director for film and television. “You use one baby for the first 20 minutes, a second baby for the next 20, etc. And if you’re doing a shot where the baby isn’t the focal point, or maybe it’s just in a crib in the background, you use a doll.”

Which results in this:

Jane Rogers explained to me that the reason casting agents go after twins or triplets isn’t just to get lookalikes for the same character (thus making the most of each newborn’s mandated 20 work minutes), but also because multiples are typically born premature. Soliciting premature babies, in other words, is a way to cast for age zero while sticking to SAG’s 15-day-old age requirement.

The money these babies earn isn't necessarily going to the parents:

“In California, with all under-18 actors you have to set up a Coogin Trust [a blocked trust account]. Any money that my daughter makes goes into that, and she gets it when she’s 18.”

The goo the "newborns" are covered in varies from set to set:

“I want to know about the cheeselike varnish,” I said.

“High fructose corn syrup,” he said. “The same sort of stuff we would use for blood if someone got shot.”

I relayed the question to my other sources and found that the substance varies set-to-set.

Jane Rogers, who does background casting for shows like Man Seeking Woman and often works with children, took time to emphasize the integrity of her goo. The goo is edible and gluten free – it is very LA. “We make sure that the goop they’re covered in is organic, water soluble, non-toxic, la-la-la.”

“We put grape jelly and cream cheese on children for birthing scenes,” Knocked Up’s producer Evan Goldberg said. “It’s weird.”

Far, far more over at the link.

Though the laws may be different in the US, the most famous UK 'baby' show - Call the Midwife - famously uses real babies for every take, but dolls for rehearsal.

More detail at Radio Times - Call the Midwife only uses real newborns for its birth scenes – but how do they cope with all the babies?

You got it right, they are using fake in most cases due to law restriction. But some times they took the scene frame from old movie or videos from net, make modifications as per their requirements.

Also sometimes for few money parents allow the camera man shoot the scene and people use mask for that frame. As there were not sound effects for that frame, it can be used directly.