By default MongoDB creates an index on the _id (ObjectId) field, but we can easily add indexes to other fields.
Using the JavaScript shell
In the JavaScript shell simply call ensureIndexUsing the 10gen drivers in C#
In C# using the 10gen drivers we can create an index using the following
collection.EnsureIndex(new IndexKeysBuilder().Ascending("artist"));
where collection is
MongoCollection<CD> collection = db.GetCollection<CD>("cds");
To remove an index we can simply use
collection.DropIndex(new IndexKeysBuilder().Ascending("Artist"));