Extending Your Stay
Generally speaking, your non-immigrant visa status can be extended while you are in the U.S. The word extension in immigration terms means that you seek to continue engaging in the same activity as a student or a scholar for which you originally came to the U.S. (same school, same lab, same degree program, etc.).
As a student your maximum extension time permissible is determined by your school's academic policy on length of degree programs, with the exception of "non-degree" students who have a limit of 2 years in most cases.
As a scholar your maximum extension time depends on the visa type. The H-1B visa has a total time of 6 years (with an exception for certain pending permanent residence cases). The J-1 visa in the Research Scholar/Professor category has a limit of 5 years. The J-1 Short-Term Scholar category has a maximum time limit of 6 months.
For more information about extensions and how to request one, check your visa type.