Create a trigger that inserts values into a new table when a column is updated

I've been looking at some previous answers on triggers on here but can't find what I need exactly but I'm sure my question has been asked/answered before.

I'm trying to keep track of any changes to columnA and columnB in table1.

If this value changes I want to keep track of the values by inserting the existing value and the new Value into a different table with a date.

I've been looking at using something like this for the insert but not sure how to add get the existing and new values of the source table (table1):

CREATE TRIGGER NewTrigger ON table1
FOR INSERT
AS

INSERT INTO table2
        (columnA , columnB, todaysDate)
    .
    .

go

I need to use (I think) the

Before update ON table1 FOR EACH ROW
   .
   .
   .
BEGIN

and look through all the changes and insert these first then do the same after the Update?