For each candidate, each voter expresses the utility of that candidates' election to them in the form of a number. In "pure" range voting, each voter may give any candidate any real number, but as the potential for Tactical voting is huge, most systems use some bounds. For example, each voter might give a real number between -1 and 1, or an integer between 1 and 10.
Counting the Votes
The scores for each candidate are summed, and the candidates with the highest sums are declared the winners.
Potential for Tactical Voting
Tactical voting is pretty much useless, especially in multiple-candidate elections. Any possibility that a favorable result will occur due to inaccurate rankings is overwhelmed by the possibility that a non-favorable result will be more likely to occur.
See also: Approval voting