By train
CityRail (http://www.cityrail.info/) trains run every hour or two to the Blue Mountains from Sydney Central, and can also connect at major stations along the way, like Parramatta. Trains run every hour or so as far as Mount Victoria and usually every second one will proceed to Lithgow. While the train will get you to the mountains, you need to determine how to get around when you get there, as there are a number of locations that you won't be able to reach without a car. That said, most of the main towns in the Blue Mountains are linked together by the rail line, and the prime tourist spots are walkable or accessible by visitor friendly bus services. See how to Get Around below.
By car
Take the M4 out of Sydney, then continue as the M4 becomes the Great Western Highway A32 on Lapstone hill. Sydney to Katoomba is 103km and takes about one hour and fifty minutes in good traffic. The traffic is much worse leaving Sydney on a Friday night, or returning to Sydney on a Sunday afternoon. Your travel time can double. After a long weekend, traffic can come to a standstill coming down the mountains into Sydney.
Hiring a car from Sydney to spend a day or two in the mountains is a popular option for visitors to Sydney, however an issue often encountered by people staying the city centre is that car rental companies along the city strip generally close before 6pm, and can have queues when they open at 9am. This can make for a very short day in the mountains. The alternative is paying for an extra days car hire, and for overnight parking in the city for two nights, which can add considerably to the cost.