Take a jug and add vodka along with crushed ice. Remember not to add too much or too less of it or else it will sabotage its flavor.
Stir the two ingredients a little and then add grapefruit. Stir it again stir with a long spoon.
Before transferring the drink into a cocktail glass, decorate it with lemon or grapefruit wedges.
You can also salt the rims which will give you a fabulous taste in every sip; this method of garnishing is used in Salty Dog Cocktail as well.
Make sure you do not use a cocktail shaker in Greyhound Cocktail because the recipe does not require a lot of stirring or shaking.