Radio contests are events in which you try to make as many contacts in a time period as possible. Contests generally take place on certain bands or using certain modes. Depending on the contest, you may score points or multipliers for different kinds of contacts.
The rules of the contest vary depending on the contest, but basically just get on the radio and start calling CQ. Here's some common rules and etiquette:
The words you would say appear with a single bar in front of the line like this.
The response of someone would typically say to you shows up like this with two bars in front of the line.
> CQ contest, CQ contest, this is Kilo Four Romeo Yankee calling CQ contest and standing by.
Whiskey One Alpha Whiskey
W1AW this is K4RY. You're coming in 5 by 9 in Southern Alabama.
K4RY you are coming in 5 by 9 in Michigan.
Thank you for the contact, W1AW. '73. K4RY.
You would log the contact and then resume calling CQ at this point.
After contesting for a while, you'll probably want to abbreviate contacts so you can make more contacts in the same amount of time. A typical contesting QSO sounds more like this:
CQ Contest CQ Contest K4RY
W1AW you're 59 in Southern Alabama.
K4RY you're 59 in Michigan.