When asking someone to dance step up to him/her and make eye contact when asking for a dance. Do not ask from a distance as it can make for an awkward moment if a number of people think they have been asked to dance, and you have to tell them that they were not.
If someone is sitting closely with their significant other, talking quietly to each other, then it is probably not a good time to ask him/her for a dance.
If someone appears to be in a normal conversation with another, you can approach, standing close and interested. When your intended partner makes eye contact, you may smile and ask "Dance?"
If two men ask the same lady to dance at the same moment, it is not recommended that either men stand down, rather that the women must choose one or the other. It is often most appropriate that the women offer the next dance to the man who was turned down. The same applies when the sexes are reversed.