Alter, meaning to change or adjust, is always a verb (except in the phrase alter ego, meaning a second self). Altar, meaning an elevated place or structure before which religious ceremonies may be enacted or on which sacrifices may be offered, is always a noun. The words are homophones, but their origins are different; alter comes from a Latin word meaning other, and altar comes from the Latin altāria.
Examples
The two words are occasionally confused, especially alter in place of the less common altar—for example:
One by one, members of the congregation filed up to the alter to receive a cross of ashes on their foreheads. [MLive]
I was 8 years old at the time and an alter boy. [Patch]
And these writers spell alter and altar correctly:
But in 2012, Macy’s said this week, it will alter its parade route, bypassing Times Square and Seventh Avenue entirely. [NY Times]
The stage was set with an altar on which there was a large photo of the Dalai Lama, and a candle burning inside a chalice. [Toronto Star]
Ministers are still engaged in a last-ditch attempt to alter the contract with the United States that obliges Britain to buy the aircraft. [Telegraph]
Gilded tombs, gleaming altars and the smell of incense all impress the Abbey’s importance as a time-honored place of worship. [CNN]