Remember the end of The Empire Strikes Back, where Leia and Luke, convalescing from surgery to replace his severed hand, gaze out of the window of a Rebel spaceship at the departing Millennium Falcon, with the Galaxy (the far, far away one) spinning slowly in the background? It looked something like this:
That's a real galaxy, though, called NGC 2841, about 45 million light years away from our own. And neither it nor its Star Wars companion would look anything like that if we were seeing them with our own eyes.
First of all, forget the spinning: it takes our solar system about 225 million years to make one rotation around the core of the Milky Way, so even if you were able to see the whole disk, it would take many human lifetimes to perceive any motion at all. Put another way, the last time we were at this spot in our rotation, Earth was in the middle of the Triassic period, the time of the earliest dinosaurs.
Maybe more importantly, I don't think we could see a galaxy in all its beauty that way at all, because it would probably be too dim for our eyes. Consider that all photos of other galaxies require pretty long exposures, even for sensitive equipment. The Andromeda Galaxy, which you can see in a dark sky with your naked eye as a faint smudge, doesn't show its full shape in a telescope until you collect light for at least a few minutes.
Consider the fact that we're right inside a galaxy, and for most of us living in cities, the Milky Way, which is the view through the thickness of our closest spiral arm, is entirely washed out by light pollution. I don't think my daughters have ever seen it, in fact. You need a pretty dark sky, preferably on a moonless night, to see it properly.
If you were far enough away from a galaxy to see the whole thing, it would be even dimmer, so no matter how dark the sky, to your naked eye it would be much more a large, galaxy-shaped smudge of light (an impressive smudge indeed, but still smudgy) than the crisp, defined, and detailed colourful disks we see in photos. You might be able to determine its shape, and see the core, but it wouldn't be what Luke, Leia, R2-D2, and C-3PO were gazing at.
People are sometimes disappointed when they look through a telescope at celestial objects. Jupiter, Saturn, the Moon, and the Sun are certainly impressive, but nebulae lack the fantastic colours and flaming tendrils we've come to expect after decades of Hubble Space Telescope images. But those pictures are long exposures, often with artificial colours displaying wavelengths humans can't even see. While those images are real, they're not what our eyes see when we look at the light directly.
Still, think about how amazing it is to do anyway: away from city lights, on a dark clear night, preferably at high altitude, you can peer up near the constellations Pegasus and Casseopeia to find the Andromeda Galaxy, no binoculars or telescope necessary (though they'll make it yet a better experience). When you see it, you know that the light hitting your eyes started its journey two million years ago, before modern humans evolved.