How are we stardust? I am a layperson and certainly not a physics student, though I'm sure that is palpably obvious.  I have a strong appreciation for people like Carl Sagan, Lawrence Krauss, and Sean Carrol.
I'm often challenged by creationists over the claim that we are all "starstuff" or "stardust".  I can understand that most or all of the atoms and things needed for life to evolve on earth came from dead starts, but how are new humans, babies, etc... the stuff of stars?
How did those star elements get into living things?  I would have thought they were only necessarily present for the early chemical-into-biological evolution.  Is there an infinite amount?  As the human population rises, do we ALL possess material from long dead stars?  Any deeper explanation and clarification would be most appreciative.  I apologize in advance for my ignorance, I hope I get some real answers, because it's a serious question.
 A: Well, people are made out of a bunch of elements, none of which are created on Earth: they all got here from somewhere else.
There are two sources for elements:


*

*Hydrogen, some Helium, some isotopes of them and I think some Lithium were made by 'primordial nucleosynthesis' within a few minutes after the big bang;

*everything else is made in stars.


So, for instance, Carbon, which is extremely important to life, was made in stars, as was Oxygen and so on.
A: The other answers so far deal with supporting Sagan's immortal "we are made of star stuff".
After accepting this assertion, the OP asks us to answer how this star stuff got into living beings. There are mechanisms for this. Many heavier elements are created in the last few moments of a star's life and dispersed throughout space in the star's supernova: the cataclysmic explosive output of energy from the production by fusion of the "starstuff" elements that make us up.
The Wikipedia Supernova Article has much relevant information, including descriptions of the nuclear processes that lead to the supernova (see also Here: Stellar Nucleosynthesis and here: Stellar evolution. 
To answer the question about dispersal, it is important to heed the quantities of energy released. The following statements are relevant:

"....the total equivalent radiant energies produced by supernovae may briefly outshine an entire output of a typical galaxy and emit energies equal to that created over the lifetime of any solar-like star."

In other words, greatly above the gravitational binding energy of most of the system. This is important, because some of the "star stuff" in question lies in layers deep within the star. The huge abundance of energy means that even this deeply buried material can be accelerated to up to $0.1 \,c$. Thus, the material can easily escape gravitational binding of the star system and coast, over time, enormous distances through the universe. The energy thus enables a thorough mixing of stellar remnants throughout the universe.
Another, less violent, mechanism applicable to AGB Stars is the thermal circulation of carbon that "dredges" the carbon to the surface throughout the star's lifetime, where it is pumped into space by thermal pulsations and radiation pressure (hat tip to user Rob Jeffries for bringing this to my attention).
Thus interstellar gas and dust clouds, after enough time, contain a great deal of the heavier, "starstuff" elements. Thus the cloud that clumped into our Sun's accretion disk and protostar contained a great deal of these heavier elements, which thus found their way into the Earth and later gave rise to its biosphere.
A: Questions like this one and this one are basically on the exact same subject.
However, to provide some precision regarding new humans, babies (let us generalize with new "beings"), let me add something.
Microscopically, beings are made of many molecules, which, in turn, are made of a bunch of atoms sticking together. These atoms can change, sometimes. I mean that their constituents may be exchanged with other atoms or particles, so that the initial "type" of the atom has been modified. We call this "nuclear reactions" because the nucleus of the atom has been modified.
There is very very very very little such change of atoms in everyday life. Only inside stars you may find sufficient energy to significantly modify the atom nuclei. This is why some say we are stardust: after the atom has exited a star, it can almost never be altered. Life, reproduction, or even modifications of the shape of the earth that can look tremendous to us, are not able to change much atoms at all. During your life, the molecules you are made of are recycled from what you eat, drink and breathe. New molecules are formed from previous ones, simply rearranging atoms in different orders. This is called chemistry, and there is no modification of individual atoms. Only their arrangement is modified.
Babies are made of molecules that come from the mother's body, and from what she ingested. there is a long chain of events like that, and you can go very far in the past without any significant change in the atoms themselves. In fact, you have to go back to the formation of the atoms inside stars. For some atoms you even have to go further than that, as most stars would not even be able to modify them: you have to go back to almost the big bang.
A: Everything the Earth is made up of was once stellar material. One 'smoking gun' pointing to this is the presence on Earth of heavier elements, including the heaviest one like uranium.
Stars convert hydrogen to helium, then helium to other elements like carbon, nitrogen etc. This process, called nuclear fusion also provides the stars' energy production. But even the largest stars cannot synthesise elements beyond iron (element No $26$). Heavier elements, including the heaviest of all, uranium) are synthesised in supernovae, when super heavy stars at the end of their fusion life collapse in an enormously energetic implosion-explosion, energetic enough to forge the heavier elements ($> 26$) from the lighter ones.
The enormous forces at play in the explosion also throw the transformed star material far and wide into the cosmos, where it will mingle with other dust and debris.
Through accretion, new stars are formed from this 'second hand' material (which now also contains the heavier elements).
Our own star, the Sun, is believed to be a second or third generation star, made from such a gas and dust cloud already seeded with the heavier elements. The planets of the solar system (or any stellar system), including our Earth, are literally the leftovers from the creation of the Sun. So the Earth and everything on it, including ourselves, are quite literally ancient star dust! Ancient may be a bit of an understatement here: the processes of stars creating iron, then followed by supernovae and re-accretion into stellar systems, takes millions and millions of years.
