How can I use optional parameters in a T-SQL stored procedure?

Dynamically changing searches based on the given parameters is a complicated subject and doing it one way over another, even with only a very slight difference, can have massive performance implications. The key is to use an index, ignore compact code, ignore worrying about repeating code, you must make a good query execution plan (use an index).

Read this and consider all the methods. Your best method will depend on your parameters, your data, your schema, and your actual usage:

Dynamic Search Conditions in T-SQL by by Erland Sommarskog

The Curse and Blessings of Dynamic SQL by Erland Sommarskog

If you have the proper SQL Server 2008 version (SQL 2008 SP1 CU5 (10.0.2746) and later), you can use this little trick to actually use an index:

Add OPTION (RECOMPILE) onto your query, see Erland's article, and SQL Server will resolve the OR from within (@LastName IS NULL OR LastName= @LastName) before the query plan is created based on the runtime values of the local variables, and an index can be used.

This will work for any SQL Server version (return proper results), but only include the OPTION(RECOMPILE) if you are on SQL 2008 SP1 CU5 (10.0.2746) and later. The OPTION(RECOMPILE) will recompile your query, only the verison listed will recompile it based on the current run time values of the local variables, which will give you the best performance. If not on that version of SQL Server 2008, just leave that line off.

CREATE PROCEDURE spDoSearch
    @FirstName varchar(25) = null,
    @LastName varchar(25) = null,
    @Title varchar(25) = null
AS
    BEGIN
        SELECT ID, FirstName, LastName, Title
        FROM tblUsers
        WHERE
                (@FirstName IS NULL OR (FirstName = @FirstName))
            AND (@LastName  IS NULL OR (LastName  = @LastName ))
            AND (@Title     IS NULL OR (Title     = @Title    ))
        OPTION (RECOMPILE) ---<<<<use if on for SQL 2008 SP1 CU5 (10.0.2746) and later
    END

The answer from @KM is good as far as it goes but fails to fully follow up on one of his early bits of advice;

..., ignore compact code, ignore worrying about repeating code, ...

If you are looking to achieve the best performance then you should write a bespoke query for each possible combination of optional criteria. This might sound extreme, and if you have a lot of optional criteria then it might be, but performance is often a trade-off between effort and results. In practice, there might be a common set of parameter combinations that can be targeted with bespoke queries, then a generic query (as per the other answers) for all other combinations.

CREATE PROCEDURE spDoSearch
    @FirstName varchar(25) = null,
    @LastName varchar(25) = null,
    @Title varchar(25) = null
AS
BEGIN

    IF (@FirstName IS NOT NULL AND @LastName IS NULL AND @Title IS NULL)
        -- Search by first name only
        SELECT ID, FirstName, LastName, Title
        FROM tblUsers
        WHERE
            FirstName = @FirstName

    ELSE IF (@FirstName IS NULL AND @LastName IS NOT NULL AND @Title IS NULL)
        -- Search by last name only
        SELECT ID, FirstName, LastName, Title
        FROM tblUsers
        WHERE
            LastName = @LastName

    ELSE IF (@FirstName IS NULL AND @LastName IS NULL AND @Title IS NOT NULL)
        -- Search by title only
        SELECT ID, FirstName, LastName, Title
        FROM tblUsers
        WHERE
            Title = @Title

    ELSE IF (@FirstName IS NOT NULL AND @LastName IS NOT NULL AND @Title IS NULL)
        -- Search by first and last name
        SELECT ID, FirstName, LastName, Title
        FROM tblUsers
        WHERE
            FirstName = @FirstName
            AND LastName = @LastName

    ELSE
        -- Search by any other combination
        SELECT ID, FirstName, LastName, Title
        FROM tblUsers
        WHERE
                (@FirstName IS NULL OR (FirstName = @FirstName))
            AND (@LastName  IS NULL OR (LastName  = @LastName ))
            AND (@Title     IS NULL OR (Title     = @Title    ))

END

The advantage of this approach is that in the common cases handled by bespoke queries the query is as efficient as it can be - there's no impact by the unsupplied criteria. Also, indexes and other performance enhancements can be targeted at specific bespoke queries rather than trying to satisfy all possible situations.

You can do in the following case,

CREATE PROCEDURE spDoSearch
   @FirstName varchar(25) = null,
   @LastName varchar(25) = null,
   @Title varchar(25) = null
AS
  BEGIN
      SELECT ID, FirstName, LastName, Title
      FROM tblUsers
      WHERE
        (@FirstName IS NULL OR FirstName = @FirstName) AND
        (@LastNameName IS NULL OR LastName = @LastName) AND
        (@Title IS NULL OR Title = @Title)
END

however depend on data sometimes better create dynamic query and execute them.