They would have to have zero similarities to any biological organism on earth.
They could maybe be carbon based, but silicon could work much better.
There is no atmosphere, so breathing is not an option. They could get oxygen from what they eat, but you may be better off coming up with a biology that doesn't need something like that, or that can recycle it all internally with minimal input.
For inputs I'd use comets, asteroids, basically any rocky/metallic body. This is why being silicon based might be a better choice than carbon, as being able to eat rocks is a big plus in an environment where carbon probably isn't readily available. Comets also have water, which and be broken down for their gasses. It's going to be cold in deep space though, so liquid oxygen and hydrogen are probably going to be better than anything that is liquid on earth. This thing might be really happy in nebulas where it could "filter feed" from the denser than average gasses.
-How did they end up in space in the first place?
So this one is a little difficult, as the odds of complex life starting on earth were abysmally low even in a very dense chemically rich soup. There really isn't much in empty space, which is why it's called empty. Maybe in some really dense nebula with a lot of star birth you could get something... but something more complex than a bacterium would be a huge suspension of disbelief.
A better explanation might be something like Mars, with really low gravity, where it had an atmosphere which gradually bled away over a really really long time, so that the creatures would gradually develop the systems it needed for living in an environment without an atmosphere. There it lived happily until something happened and the planet started to break up (maybe a new star was born near by?), scattering the creatures out into space, where they fed on the shattered remains of their planet, before moving on.
One thing that would have helped them is if they also received energy from starlight, and so developed giant solar collector fins that they could deploy, which by chance also worked really well as solar sails once they were let loose.
Once again being in a stellar nursery would be a good thing as the outward pressure would help move them into deep space faster. It would take a REALLY long time to spread galaxy wide, but it could be that they travel from star to star, eating the outermost kupiter type objects, reproducing en mas, and then spreading out to all the next closest stars.
An interesting side thought... these things could be an explanation for panspermia. Say they had a carbon based single cell life form that found a way to incubate inside of them once the planet started to die, and which spreads to the remnants of comets and other kupiter belt objects that it feeds on, and those happen to fall in and occasionally collide with planets, then you could end up with these things spreading life across the universe, and be an explanation of divergent evolution across lots of star systems.