The best way is to make note of your confirmation number(s) - you will need to enter this on the new reservation. Then, check for new flights. When you see what you want to book and have checked for availability, open a new browser and go through the whole process, up to the payment page. Go back to your original reservation and "cancel" - it will confirm your cancellation, telling you the expiration date to re-use the funds from your canceled flight (travel must be completed within one year from original booking date). Go back to your payment page for the new flight and enter the old confirmation number and name where it says "Apply funds." If you owe any additional money, it will let you know. If the new flight is cheaper, it will show you any remaining credit for future travel. The travel funds only may be used for the same person named on the original reservation.
It's better to cancel and rebook, than to just "change," so that you can get a refund on any portion that's refundable, usually taxes and fees.
If you booked with points, you can just "change" the reservation, if you don't care about the taxes and fees being refundable, if new trip is completely canceled.
Remember, that you can cancel a trip and get a full refund, if cancelled less than 24 hours from time of booking, if you change your mind.