You can drive to the top. That way takes you through narrow winding roads with beautiful views on either side of the mountain.
You can hike up to the top. I was told that takes about 90 minutes from a shrine near the base. We were running out of daylight when I was there, so that wasn't an option.
Your third option is the Nagasaki Ropeway! Sadly, it was closed for maintenance the day we were there. I was told that it was to re-open on the 16th of December.