How is the Milky Way Galaxy classified?
The Milky Way is classified as a SBc Galaxy
There are many types of galaxies, which I won't go into here but in terms of our galaxy it is a SBc type.
SBc's meaning is as follows:
"S" stands for Spiral (shape looks like a spiral)
"B" stands for Barred (meaning that in the center of the spiral there is a rectangular shaped cluster of stars.
"c" stands for type c of the SB Galaxy, meaning that it's spiral arms are separated with open space between them i.e. no stars in the spaces.
Here's a pic showing the types of Galaxies:
*SBc is at the bottom right of the picture
Image from: http://astro.wku.edu/astr106/galaxy.html
In terms of classifying it since we can't actually see our full galaxy from a distance, scientists I would think look at our galaxy from Earth's perspective and determine the type of galaxy in that manner, i.e. looking at the center of our galaxy to see if there is a bar shape and determining whether or not there are spaces between the spiral arms.
Hope I helped :)