For the galaxies, I use a sponge. My preference is to use a sponge-brush from the craft store; I snip the polished part off every time I finish with that color, so I can use the sponge over and over. For galaxies, it gives a great coarse, cloudy texture. You can use them for gradients too, although you don't get as nice of a blend as you might with a makeup sponge.
I like to use holographic polishes for the galaxy clouds, because I think it adds a little extra depth when the sun hits it. I sponged Color Club Revvvolution first, in stripes/streaks to serve as a base for the galaxy clouds. I added little patches of Milani Cyberspace to add a little cool sparkle shimmer; the blue doesn't really translate to the nail when the polish is such a thin coat, but it adds a little rainbow shine that I love.
I added little patches of Anise Total Temptress, a dusty dark lilac, mostly around the edges of the nail so it looks like the centers of the stripes are more solid than the edges. At least one opaque polish helps a lot to get the look just right, although I think too much opacity can ruin the dreamy space-like quality. However, I'm just one person, and some people probably really like a more opaque, in-your-face galaxy look. Variety is the spice of life!
I added a little shimmer with the Revlon Colada Fizz, just to soften all the outlines and make sure it looked as hazy as I wanted it to. Also, now my nails smell fruity and awesome :)
Pirouette my Whistle, or any other sparse-ish white glitter, is great for quickly adding stars. Alternatively, you can use a brush or dotting tool to add little stars to your galaxy to give the illusion of distance. A hard line around the star could be softened with a quick touch of a sponge, to give it a little halo like an actual star would have.
As you can see by the last two pictures, this is messy and will require cleanup. An angled brush dipped in acetone (not a remover with glycerine or scents in it, but pure acetone, otherwise it'll just smear polish around on your hand [at least in my experience]) After cleanup, you'll have this:
And after you snip the used portion of your sponge off, you'll have this:
I chose cool tones for my galaxy, but you definitely have all kinds of color options; space is not uniform, it's pretty majestically varied, so try warm colors, or all yellows, or all greens, reds, oranges, silvers, etc.!