Check if extended property description already exists before adding

This first script checks if the extended property describing the table exists:

IF NOT EXISTS (SELECT NULL FROM SYS.EXTENDED_PROPERTIES WHERE [major_id] = OBJECT_ID('Table_Name') AND [name] = N'MS_Description' AND [minor_id] = 0)
EXECUTE sp_addextendedproperty @name = N'MS_Description', @value = N'This table is responsible for holding information.', @level0type = N'SCHEMA', @level0name = N'dbo', @level1type = N'TABLE', @level1name = N'Table_Name';

This second script checks if the extended property describing the column exists:

IF NOT EXISTS (SELECT NULL FROM SYS.EXTENDED_PROPERTIES WHERE [major_id] = OBJECT_ID('Table_Name') AND [name] = N'MS_Description' AND [minor_id] = (SELECT [column_id] FROM SYS.COLUMNS WHERE [name] = 'Column_Name' AND [object_id] = OBJECT_ID('Table_Name')))
EXECUTE sp_addextendedproperty @name = N'MS_Description', @value = N'This column is responsible for holding information for table Table_Name.', @level0type = N'SCHEMA', @level0name = N'dbo', @level1type = N'TABLE', @level1name = N'Table_Name', @level2type = N'COLUMN', @level2name = N'Column_Name';

Here is another stored procedure approach, similar to Ruslan K.'s, but that doesn't involve try/catch or explicit transactions:

-- simplify syntax for maintaining data dictionary

IF OBJECT_ID ('dbo.usp_addorupdatedescription', 'P') IS NOT NULL
    DROP PROCEDURE dbo.usp_addorupdatedescription;
GO

CREATE PROCEDURE usp_addorupdatedescription
        @table nvarchar(128),  -- table name
        @column nvarchar(128), -- column name, NULL if description for table
        @descr sql_variant     -- description text
AS
    BEGIN
        SET NOCOUNT ON;

        IF @column IS NOT NULL
            IF NOT EXISTS (SELECT NULL FROM SYS.EXTENDED_PROPERTIES
            WHERE [major_id] = OBJECT_ID(@table) AND [name] = N'MS_Description'
                  AND [minor_id] = (SELECT [column_id]
                                    FROM SYS.COLUMNS WHERE [name] = @column AND [object_id] = OBJECT_ID(@table)))
                EXECUTE sp_addextendedproperty @name = N'MS_Description', @value = @descr,
                                               @level0type = N'SCHEMA', @level0name = N'dbo', @level1type = N'TABLE',
                                               @level1name = @table, @level2type = N'COLUMN', @level2name = @column;
            ELSE
                EXECUTE sp_updateextendedproperty @name = N'MS_Description',
                                                  @value = @descr, @level0type = N'SCHEMA', @level0name = N'dbo',
                                                  @level1type = N'TABLE', @level1name = @table,
                                                  @level2type = N'COLUMN', @level2name = @column;
        ELSE
            IF NOT EXISTS (SELECT NULL FROM SYS.EXTENDED_PROPERTIES
            WHERE [major_id] = OBJECT_ID(@table) AND [name] = N'MS_Description'
                  AND [minor_id] = 0)
                EXECUTE sp_addextendedproperty @name = N'MS_Description', @value = @descr,
                                               @level0type = N'SCHEMA', @level0name = N'dbo',
                                               @level1type = N'TABLE', @level1name = @table;
            ELSE
                EXECUTE sp_updateextendedproperty @name = N'MS_Description', @value = @descr,
                                                  @level0type = N'SCHEMA', @level0name = N'dbo',
                                                  @level1type = N'TABLE', @level1name = @table;
    END
GO

I wrote simple stored procedure to add or update extended property 'MS_Description':

IF OBJECT_ID ('dbo.usp_addorupdatedescription', 'P') IS NOT NULL
    DROP PROCEDURE dbo.usp_addorupdatedescription;
GO

CREATE PROCEDURE usp_addorupdatedescription
    @table nvarchar(128),  -- table name
    @column nvarchar(128), -- column name, NULL if description for table
    @descr sql_variant     -- description text
AS
BEGIN
    SET NOCOUNT ON;

    DECLARE @c nvarchar(128) = NULL;

    IF @column IS NOT NULL
        SET @c = N'COLUMN';

    BEGIN TRY
        EXECUTE sp_updateextendedproperty  N'MS_Description', @descr, N'SCHEMA', N'dbo', N'TABLE', @table, @c, @column;
    END TRY
    BEGIN CATCH
        EXECUTE sp_addextendedproperty N'MS_Description', @descr, N'SCHEMA', N'dbo', N'TABLE', @table, @c, @column;
    END CATCH;
END
GO

Maybe my answer did not directly connect to this question, but I would like to point out that MS_Description is actually case sensitive, even we add it with SQL. If we use MS_DESCRIPTION instead of MS_Description, it will not show up in the SMSS table design view.

In my case, I have to do something like this to removed the existing description and add a correct one.

IF EXISTS (
    SELECT NULL
    FROM SYS.EXTENDED_PROPERTIES
    WHERE [major_id] = OBJECT_ID('TableName')
        AND [name] = N'MS_DESCRIPTION'
        AND [minor_id] = (
            SELECT [column_id]
            FROM SYS.COLUMNS
            WHERE [name] = 'ColumnName'
                AND [object_id] = OBJECT_ID('Tablename')
            )
    )
    EXEC sys.sp_dropextendedproperty @name = N'MS_DESCRIPTION'
        ,@level0type = N'SCHEMA'
        ,@level0name = N'dbo'
        ,@level1type = N'TABLE'
        ,@level1name = N'TableName'
        ,@level2type = N'COLUMN'
        ,@level2name = N'ColumnName'
    GO

EXEC sys.sp_addextendedproperty @name = N'MS_Description'
,@value = N'Description detail'
,@level0type = N'SCHEMA'
,@level0name = N'dbo'
,@level1type = N'TABLE'
,@level1name = N'TableName'
,@level2type = N'COLUMN'
,@level2name = N'ColumnName'

GO