How does gravity work in space?

The amount of gravity that each particle in the universe possesses is determined by its mass, or in the case of large objects, by the combined action of billions upon billions of particles.

The moon remains in its orbit because of the earth's gravitational pull, which is felt far beyond the moon.

Regarding the sun, its gravitational pull extends beyond Pluto's orbit and the Kuyper Belt.

In the case of the Milky Way Galaxy, the galaxy's black hole's gravitational pull reaches beyond the galaxy's furthest-reaching star.

The earth is essentially affected by the gravitational pull of both the sun and the black hole. This implies that, depending on the mass of the objects affecting you, you will always be subject to multiple gravitational forces simultaneously, wherever you are in the galaxy.

Peter gave you the classical answer. In case you meant to ask in the relativistic sense, here is the General Relativity answer.

Gravity makes itself felt by curving spacetime. A particle subject to gravity is following a "straight" path, that is the shortest path in a space where straight lines are no longer straight. What curves them is the presence of a mass such as the sun.

To find out how much space is curved is to solve Einstein's equations. These are the usual coupled equation:

Matter generates curvature Curvature affects matter

The first equation is of the form

Stress-Energy Matter Tensor = curvature

which you need to integrate to get the geometry of space modified by the presence of matter. Integrating gives you the metrics. The metrics is a tensor which describes the difference between one meter in the x direction and one meter in the y direction, or one meter near the sun and one meter far away. These differences are coded in the form of coefficients which you stick into the equation describing a straight line et voila, the equation now describes a curved line.

In reality, things are more complicated, Because the sun cannot affect the earth at a distance but through the exchange of energy and momentum, that exchange being made by the emission and reception of gravitational waves, of, in quantum language, of gravitons.

Gravity in space works similarly to how it does on Earth, but with some differences. Gravity is a fundamental force that attracts objects with mass toward each other. In space, large objects like planets and stars exert gravitational forces on nearby objects, causing them to orbit around them. The strength of gravity depends on the mass of the objects involved and the distance between them, following Newton's law of universal gravitation and Einstein's theory of general relativity. In the absence of significant gravitational forces from nearby objects, objects in space experience microgravity, where they appear weightless.