There's no "Christian" answer to the question. It's like asking "What do Christians think about J.J. Abrams directing the new Star Wars movie?"
That said you are more than likely going to come into contact with roughly three distinct positions:
1) The earth is as old as modern science has dated it, and therefore is roughly 4.5 billion years old.
2) The earth is old, perhaps hundreds of thousands or millions of years old. This is roughly the position of Old Earth Creationists, it's a position that was much more common before the middle of the 20th century. The majority of the original Fundamentalists were Old Earth Creationists.
3) The earth is no more than 10,000 years old, probably only 6,000, based on Ussher's Chronology that adds the years of the patriarchs together. Known as Young Earth Creationism. It became incredibly popular in the United States following the publication of The Genesis Flood in the 1960s.
You may find other positions, but more-or-less these are the three that one will consistently encounter among Christians.
Because there is no "official" "Christian" position on the topic. There never has been.
-CryptoLutheran