What tenets must a person accept to be a Buddhist? I'm curious what minimal tenets a person must accept in order to be considered a Buddhist. 

As an example of the type of answer I'm looking for, I'll give you the minimal tenets of Christianity as I know them. A person must...


Accept that there is only one God and that Jesus, his son, walked the Earth for some time in order to be a model for his followers.  
Accept Jesus/God as their lord and savior. 
Recognize that they are born in a state of sin, and that acceptance of Jesus/God is the one and only way to attain a happy eternal life.


Is there a similar set of statements that can be made about Buddhism?
You just need to take refuge in the Triple Gem sincerely.


Buddham saranam gacchami - I go to the Buddha for refuge. 
Dhammam saranam gacchami - I go to the Dhamma for refuge.
Sangham saranam gacchami.- I go to the Sangha for refuge.


Refuge here means spiritual refuge. It doesn't mean you reject medicine for physical ailments like in some Christian sects.

Taking refuge will be broken for ordinary people when they die, but this breaking is blameless and does not bring bad results. On the other hand, breaking the taking of the Triple Refuge during one's life is very serious. This is broken whenever a person goes for refuge to a teacher outside the Buddha's Dispensation or when a person is disrespectful to the Triple Gem. Those who are Noble Ones will never break with their refuge. But ordinary people, through ignorance, doubt, and wrong knowledge about the special qualities of the Buddha, the Dhamma, and the Sangha, are susceptible to breaking their refuge. 

Read more at How to Take the Triple Refuge.