This has been fairly common scenario & simple too, however i just thought to put up all the options that we have for this & some considerations about them. Here it goes

Option 1: New Storage Drive in Addition to Existing Drive

1.      Stop all SharePoint related IIS web sites
2.      The following Services had set to Stopped

3.       Bring the SharePoint Site Content Database Offline
4.       Open SQL Server Management Studio

•       Expand the Databases section
•       For the SharePoint database we need to move, we must perform the following:
          1. Right click the database
          2. Click on Properties
          3. Select Files from the left hand pane
          4. Make note of the Path
          5. Click on Cancel
          6. Right click again the database
          7. Select Tasks -> Detach.
       8. Click the checkbox for Drop Connections. By default, the checkbox for keep Full Text Catalogs should be checked. Make sure that is true.

5.       Move the LDF & MDF files from the path noted in Step # 4  to the new Drive location

6.       Attach the moved files to the Site  Content database using SQL Management Studio

7.       Bring the database back Online

8.       Start the SharePoint Services that were stopped in step # 2

9.       Start the IIS Web Sites

Considerations: With this Method we cannot move the SharePoint _ Config database & SharePoint Search databases. This option should only be chosen if we just need to move the Site Content database which is growing in size currently

 Option 2: Adding a new Storage which will finally replace the existing drive that contains database

1.      Stop all SharePoint related IIS web sites from the SharePoint Web Server

2.      The following Services have to be stopped.
        -Windows SharePoint Services Administration
        -Windows SharePoint Services Timer
        -Windows SharePoint Services Search

        -Windows SharePoint Services Tracing

        - Office Document Conversions Launcher Service

        - Office Document Conversions Load Balancer Service

        - Office SharePoint Server Search

        - Indexing services
        - IIS Admin Service

3.       Stop the MS SQL Service on the SQL Backend

4.       Move All the SQL Database from “P” Drive to the new “X” Drive

5.       Change the Drive Letter of “P” Drive to “Y” Drive

6.       Change the Drive Letter of “X” Drive to “P” Drive.

7.       Start the IIS Web Sites that were stopped in Step # 1

8.       Start the SharePoint Services Listed in Step # 2

9.       Start the MS SQL Service on the SQL backend