The Grand March is often used to start off a ball. It is simply a march around the room with a partner, usually to the music of a piper. When the Grand March is announced, find a partner and line up. If they've come with a date, most people partner up with that person for the Grand March, but if you've come alone don't feel bashful about just asking someone. It doesn't matter if the person is the same sex.
Many people consider it rude to do so for the whole evening.
Feel free to ask anyone of either sex to dance. It is customary to dance with many different partners throughout the evening. Beginners shouldn't be afraid to ask more experienced dancers to dance. Form sets when the dance is announced or the band signals the next dance by playing the opening bars of music. It is considered rude to take the floor before one of these two signals has been given.