When we went a couple of years ago, we just got a train from Central Station in Sydney to Katoomba. Dead easy.
Here is the timetable:-
http://www.cityrail.info/timetable/ttable.jsp? line=bm&day=wd&dir=dn
Trains seem to run once an hour or so. They take about 2hours from Central to Katoomba.
Once in Katoomba it is a short walk from the station to the town, including shops / accomodation etc.
We stayed at the YHA in Katoomba, and it was probably one of the best YHA's I have stayed in, highly recommended:-
http://www.yha.com.au/hostels/details.cfm?host elid=183