There is no right to marriage -- gay marriage, same sex marriage, heterosexual marriage -- guaranteed in the Constitution. In fact, marriage is not mentioned in the Constitution at all, which means the federal government has no role in marriage as a construct.
Per the Tenth Amendment to the Constitution:
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
Because the Constitution does not grant the federal government any authority with regards to marriage, the Tenth Amendment explicitly leaves that power with the individual states.
My state can discriminate against gay folks who want to marry?
It certainly can. Nothing in the Constitution prohibits individual states from defining marriage any way they choose. One state may embrace marriage between two people of the same sex; another state may recognize only heterosexual marriage between one man and one woman; a third state could even choose to legalize polygamy if it wishes.
Currently most states have not legalized gay marriage. Those that have include Connecticut, Iowa, Massachusetts, New Hampshire, New York, and Vermont, plus Washington, D.C.
Doesn't the Fourteenth Amendment's "Equal Protection" clause challenge this reading?
No. The Fourteenth Amendment, to this end, guarantees three things: 1) that states do not pass laws that exclude specific individuals and groups (i.e. banning a gay man from marrying a wo