How to declare a variable in SQL Server and use it in the same Stored Procedure

I can see the following issues with that SP, which may or may not relate to your problem:

• You have an extraneous ) after @BrandName in your SELECT (at the end)
• You're not setting @CategoryID or @BrandName to anything anywhere (they're local variables, but you don't assign values to them)

In a comment you've said that after fixing the ) you get the error:

Procedure AddBrand has no parameters and arguments were supplied.

That's telling you that you haven't declared any parameters for the SP, but you called it with parameters. Based on your reply about @CategoryID, I'm guessing you wanted it to be a parameter rather than a local variable. Try this:

CREATE PROCEDURE AddBrand
   @BrandName nvarchar(50), -- These are the
   @CategoryID int          -- parameter declarations
AS
BEGIN
   DECLARE @BrandID int

   SELECT @BrandID = BrandID FROM tblBrand WHERE BrandName = @BrandName

   INSERT INTO tblBrandinCategory (CategoryID, BrandID) VALUES (@CategoryID, @BrandID)
END

You would then call this like this:

EXEC AddBrand 'Gucci', 23

or this:

EXEC AddBrand @BrandName = 'Gucci', @CategoryID = 23

...assuming the brand name was 'Gucci' and category ID was 23.

CREATE PROCEDURE AddBrand
@BrandName nvarchar(50) = null,
@CategoryID int = null
AS    
BEGIN

DECLARE @BrandID int = null
SELECT @BrandID = BrandID FROM tblBrand 
WHERE BrandName = @BrandName

INSERT INTO tblBrandinCategory (CategoryID, BrandID) 
       VALUES (@CategoryID, @BrandID)

END

EXEC AddBrand @BrandName = 'BMW', @CategoryId = 1