There's two options for you.
One way is you have a stored procedure that will take the table name, and will have a series of IF-ELSE statements, each of which simply invokes a stored procedure that handles that particular table.
The other way is to use dynamic SQL. You can use the sp_executeSQL command. See this page for more details: http://msdn.microsoft.com/en-us/library/ms188001.aspx.
Basically you'd do something like this:
CREATE PROCEDURE sp_DynamicSQL
DECLARE @Statement VARCHAR(MAX)
SET @Statement = 'SELECT * FROM ' + @TableName ' WHERE 1 = 1 '
EXEC sp_executeSQL @Statement
More details on the exact functionality can be found on that page.