Binary and multiple-star systems aren't rare exceptions in the galaxy — by some estimates, roughly half of all Sun-like stars have at least one stellar companion. That means the question 'what if Earth had two suns' isn't purely hypothetical; astronomers study real systems that answer close variations of it every year.
It's really two different questions
The outcome hinges on orbital architecture. In a wide binary, the second star could be dozens or hundreds of astronomical units away — for reference, Alpha Centauri A and B, the closest real binary pair to Earth, orbit each other at a distance ranging between roughly 11 and 35 AU (1 AU is the Earth-Sun distance, about 150 million km). A planet close to one star in a wide pair like this would experience its home star normally, with the companion showing up as an unusually bright point of light, sometimes bright enough to cast faint shadows at night.
The far more dramatic version is a close binary, where a planet orbits both stars together — what astronomers call a circumbinary orbit. This isn't speculation: Kepler-16b, discovered in 2011, is a real planet orbiting two stars that eclipse each other every 41 days, and several more circumbinary planets have been confirmed since.
Confirmed circumbinary planets, including Kepler-16b and Kepler-1647b, are documented, peer-reviewed discoveries from NASA's Kepler mission — not theoretical models. Their existence proves stable two-star planetary orbits are physically possible, at least under the right geometric conditions.
What daily life would look like
On a genuinely circumbinary Earth, the two suns would rise and set at different times as they orbit each other, producing days with two dawns, two dusks, or occasionally near-simultaneous ones, depending on the point in the binary cycle. Shadows would frequently split into two, at different angles and darkness levels. If the stars occasionally eclipsed one another from the planet's point of view — as Kepler-16's stars do — the combined light output would visibly dim on a predictable schedule.
The orbital stability problem
This is the part science fiction usually skips. For a planet to maintain a stable orbit in a binary system, it generally needs to sit either very close to one star (well within the gravitational dominance of that star, ignoring the other) or far enough out from both stars to orbit their common center of mass smoothly, beyond what astrodynamicists call the critical stability radius. Planets caught in between tend to get gravitationally perturbed onto chaotic or ejected orbits over time. This is a genuine constraint astronomers use, described in stability criteria such as those developed by researchers like Holman and Wiegert (1999), when assessing whether a real exoplanet candidate in a binary system could actually be habitable long-term.