How do I create a conditional WHERE clause?

Based on the script in question, it seems that you need the condition for Column1 irrespective of whether the variable @booleanResult is set to true or false. So, I have added that condition to the WHERE clause and in the remaining condition checks whether the variable is set to 1 (true) or if it is set to 0 (false) then it will also check for the condition on Column2.

This is just one more way of achieving this.

Create and insert script:

CREATE TABLE MyTable
(
    Column1 VARCHAR(20) NOT NULL
  , Column2 VARCHAR(20) NOT NULL
);

INSERT INTO MyTable (Column1, Column2) VALUES
  ('value1', ''),
  ('',       'value2'),
  ('value1', 'value2');

Script when bit variable is set to 1 (true):

DECLARE @booleanResult BIT
SET @booleanResult = 1

SELECT      *
FROM        MyTable
WHERE       Column1 = 'value1'
AND         (        @booleanResult = 1
                OR  (@booleanResult = 0 AND Column2 = 'value2')
            );

Output:

COLUMN1 COLUMN2
------- -------
value1  
value1  value2

Script when bit variable is set to 0 (false):

DECLARE @booleanResult BIT
SET @booleanResult = 0

SELECT      *
FROM        MyTable
WHERE       Column1 = 'value1'
AND         (        @booleanResult = 1
                OR  (@booleanResult = 0 AND Column2 = 'value2')
            );

Output:

COLUMN1 COLUMN2
------- -------
value1  value2

Demo:

Click here to view the demo in SQL Fiddle.

You can group conditions easily in a WHERE clause:

WHERE
   (@BooleanResult=1 AND Column1 = 'value1')
OR
   (@BooleanResult=0 AND Column1 = 'value1' AND column2 = 'value2')

Could you just do the following?

SELECT
    *
FROM
    Table
WHERE
    (@booleanResult = 1
    AND Column1 = 'value1')
OR
    (@booleanResult = 0
    AND Column1 = 'value1'
    AND Column2 = 'value2')