I caught the 6:20 Blue Mountains Line train from Sydney Central Station to Katoomba station yesterday for AUD$5.95 using the Opal Card. It arrived on time at around 8:22 am. I then walked to Scenic World from the train station down Katoomba Street and onto Katoomba Falls Road. I found the route very well signposted and it was an easy stroll of around 30 minutes to arrive at Scenic World in time for opening at 9:00 am. I'd pre-purchased my Scenic World ticket on their website for AUD$39 as a weekday (I think it is more at the weekend). There were not many there at the beginning of the day but the numbers certainly increased throughout the day. If your knees are up to it, I would highly recommend walking the Furber Steps walkway down to the valley floor. There are spectacular views as you descend the 200+ meters, and with the Scenic World discovery pass you can ride up on either the Railway or Gondola. Note that there are no toilets or water available on the descent nor at the bottom - you need to walk or ride back up to the Scenic World main base at the top of the cliffs to use the facilities there.
I'd planned on staying for three hours, but the scenery was so spectacular I ended up staying until around 1.30 pm. I caught the 686 bus (again using the Opal card) from Echo Point back to the railway station for AUD$2.15 one way. The stop was outside the shop near the entrance to the Echo Point lookout - you'll see a big line of tourist buses and the bus stop is closest to the corner. The bus took a circuitous route and looped back on itself. I caught the express train back to Central Station at 2:04 pm for $3.95.
Overall I was really surprised how spectacular the views were, even having previously seen the videos. The cicadas, birds and waterfall noise made it a very special place. Seeing the cockatoos flying around the valley was amazing as well.