I've read about a trail to get to the Cristo Redentor, but I'm not sure about the safety of a trail like this in Rio de Janeiro. Tours to the Corcovado are very expensive and the cable car is not significantly cheaper than these. The wikitravel talks about the lines 583 and 584 (from Copacabana and Ipanema to Corcovado railway station), but don't explains if these lines arrives to the Cristo Redentor and the travel price (and if you have to pay an extra ticket once you arrive).
The city bus to Corcovado railway station (Cosme Velho street) stops at the lower station of cable car. Link to Google Maps with this bus stop.
The cable car is one option. AFAIK, price is R$43 per adult, which is around 21 USD.
There is also a road to the top, but city buses don't go there. At the station you can usually also find people that will offer you ride with their minibuses. The price is comparable to cable car. It may be cheaper if you are in larger group, so you can hire whole car.