If you have the swing vote in an election, you should do just what you should do every time you vote. Your thought process should not be any different.
Any time that you vote, you should take the time to become informed about the issues and/or the candidates. It is important that people should not vote simply based on whims or on name recognition. Such mindless voting reduces the quality of our democracy. Therefore, whether you have the swing vote or not, you should take the time to educate yourself. Having gathered as much information as you need, you should vote based on what you think is best for the country (or the state or whatever level of government you are voting for).