The current accepted answer literally just tells you now to set a single column's default value to NULL. I'm sure you already knew how to do that?
I believe though that you're asking how to set the default value of every single column in every single table in the database which does not already have a default value of NULL, in one go, to save time.
You can do the following
SELECT
CONCAT(
'ALTER TABLE ', table_name,
' MODIFY COLUMN `', column_name, '` ',
data_type,
IF(data_type IN ('varchar', 'char'), CONCAT('(', character_maximum_length, ')'), ''),
' NULL DEFAULT NULL;'
) AS alter_statement
FROM information_schema.columns
WHERE table_schema = 'YOUR_DATABASE_NAME'
AND column_default IS NULL
AND is_nullable = 'YES';
This will return an alter statement for every column which does not have a default value, you can copy the statements, use search and replace to remove the quotes around the strings. Now you have probably hundreds of alter statements ready to fire off. You can for example paste them into SQLWorkbench and click "run" and it will run them all and update everything in under a second.
Note that it will also give alter statements for columns which already have a default value of NULL, as well as the requirement of columns which don't have any default value. But since there's no harm of altering a column to have a default value of NULL if it already has a default value of NULL, then that doesn't matter.
Look over the alter statements first though to make sure it all looks ok.
noneis not any special value in MySQL of which I'm aware. Can you add sample data which explains what you are trying to do here?