Finding exact row in Clustered index leaf page
The specifics of how SQL Server does it is not public. 

But I recommend you read the vast research material on the subject which is public. Modern B-Tree Techniques is a good start. Many more papers from Goetz Graefe talk about this area, he is well known in the industry. 

Interpolation search is a well known technique in B-Trees and there is plenty of material detailing possible approaches (bear in mind that none of the papers describe explicitly how SQL Server does it and there are many ways to skin a cat).