It is widely accepted that the universe is about 13.8 billion years old give or take a million or so. No one actually knows precisely how old the Universe really is, it is the best calculation so far. Before that date, there was nothing, there's speculation that there might have been something before then, another universe or just plain nothingness.
We can't be exactly certain as to how old the oldest star is and which one it is. We can only calculate the best guess on which is the oldest. Methuselah Star is the strongest candidate at the moment for being the oldest surviving star.
Immediately after the Big Bang, no stars began forming. According to N.A.S.A.s Wilkinson Microwave Anisotropy Probe in 2003, the earliest stars formed 200 millions years after the Big Bang once the universe had began cooling down and that allowed matter to form and ultimately star, galaxies, etc. 200 million years is merely a blink in the eye when talking about time of the universe. Ref: Starchild
Scientists are able to determine the age of the object by looking at the redshift, how much of the stars spectrum is red. The redshift also tells how much the object be it star or galaxy has shifted in the universe since the light was produced. It is hampered by the fact we can't directly observe the birth of the early universe. The only person who could is the fictional character The Doctor from the television series Doctor Who using his space ship, the TARDIS. Ref: Scientific America
By looking at the Cosmic Background Radiation (CBR), Cosmologists have been able to make deductions about the early universe. The CBR is believed to have been created some 400,000 years after the Big Bang. The Big Bang is the term used to describe the moment that the Universe began its life, in other words its birth. At the beginning soon after the Big Bang, there was a dark period when nothing happened. How long the Dark period lasted is open to speculation which according to Starchild was about 200 million and new research based on the Hubble Deep Field, the dark age ended much later at 500,000 years after the big bang. Ref: Brian Koberlein
Stars can be generated into Populations based on their age and metal content. The classification system was first devised by Walter Baade who came up with Population I and II after he was studying the Andromeda Galaxy. Population III was added later. Ref: Encyclopedia.
Population III are the oldest stars in the universe but are only hypothetical as none have been observed. These stars would be the first stars to have been created in the early universe. They would have been massive compared to the stars of today, maybe 1000 times the mass of our Sun. Having a large mass means they would have had a relatively short life-time, millions instead of billions of years like our Sun. You might think having more fuel would keep a star going for longer but the most fuel efficient stars are small stars.
When the Population III stars exploded in supernova, they would have generated a lot of heavy elements which would have been ejected out into space to be picked up in gas clouds elsewhere and pulled into the next generation of stars. Population III stars are hot, extremely large and would have been blue stars. The Population III stars would have probably been bigger than UY Scuti which is widely recognised as being the largest star so far discovered and is 1,700 times the size of our Sun. If you thought our Sun was massive, its nothing compared to UY Scuti.
Population II stars are generally thought to have been created about 100 million years after the Big Bang. These stars can be found generally near the centre of the Milky Way or at the very edge of the Milky Way Galaxy. There are some stars that are younger than the Sun that belong to this group, example of one is Mu Cassiopeia.
These stars are said to have low metal content, this means that these stars are metal-poor where they have low amounts of gases such as carbon, nitrogen, oxygen and neon. Metallicity is fraction as depicted as a decimal of the amount of a star that is not hydrogen or helium. It is normally deduced by looking at the star's light spectrum. Ref: Wiki.
The third and final group is Population I which are young stars with a high amount of metal in them. Our Sun is estimated at being about five billion years old, its not that young but belongs to an intermediate group that contains these middle-aged stars. The more extreme members of this group are stars that are less than 100 million years old. An example of a Population I star is Cervantes.
Our Star, the Sun is believed to have been created when a supernova exploded causing the nebula where the Sun is located today to collapse and create the Stars and planets today. Therefore the materials created in the supernova would have picked up and included in our Star and created the planets and then ultimately the life that exists on this planet.
We can never really be sure what is the oldest star in the Universe but Methuselah Star is widely seen as being the oldest star so far discovered. It had at one time been calculated as being older than the Universe at 16 billion years old before being revised down to 14.5 and then to 13.7 billion, a mere 100 million years after the Big Bang. Although mentioned earlier the first stars would have been blue, this star isn't. The star is located in the constellation of the Zodiac sign Libra.
In the video linked earlier, the video mentions star SM 0313 in Hydrus being older, there's probably nothing much in it if anything and Methuselah Star is generally considered to be older. It will be hard to prove definitively which is older. Ref: Wiki
The name SM 0313 comes from it being studied by Star Mapper and its coordinates. HE stars are named after the Hamburg/ESO survey. A lot of old stars are prefixed with the letters HE such as HE 0437-5439 which although is only a young Population I, its mentioned here as an example of a HE star.