Complex sentence: An unmixed liquor served is shaken or stirred with ice to chill it before serving it without the ice, while liquors or mixed drinks can be served "up", in a stemmed glass.
Split into simpler sentences: An unmixed liquor served "straight" has been shaken or stirred with ice to chill it before serving it without the ice. Liquors or mixed drinks can be served "up", meaning that they are served in a stemmed glass.