What's better than making an awesome style for your feature layers? Being able to easily share and reuse them. Both vector and raster styles can be saved and reused—however, in slightly different ways.
For this recipe, you need two similar vector layers and a set of two similar raster layers. In the example data that is provided, use two of the bus route shapefiles and two of the elevation rasters (for example, elevlid_D782_6.tif).
First we'll start by copying and pasting styles for vector layers:
Try to copy and paste the style of one bus route to the second bus route using the right-click menus:

.qml) or SLD File.... Both formats are XML text files, QGIS Layer Style... is recommended for maximum compatibility:
Rasters are slightly trickier in that you can save a symbology file, but you can also save a color table. The color table is a text file that lists raster value ranges and associated color codes. It's a much simpler format to hand-edit than XML (QGIS Layer Style File), but does not retain things like transparency or classification settings:
.txt file with the disk button (above the color table on the right end of the button row; refer to the screenshot).
Normally the style information for a layer is saved in the .qgs (if you save your project) project file. The various export methods just package up the style information for a layer into a separate file in a generic manner (not associated with the original data). This lets you apply similar styles to similar data sources.
Vector symbology is stored in a special XML file that ends in the .qml extension. You can read or edit the file if you want, and it can be produced via scripts or copied and pasted to create mashups of multiple styles.
Raster symbology can also be stored in a .qml file. However, there's an additional option to export the classification ranges and colors to a simple text file, one value or range of values and one color code per line.