By car
There are four ways by car from Christchurch into Lyttelton:
Through the Lyttelton Road Tunnel. The Tunnel is probably the best bet if you're unfamiliar with driving on the left and squeamish about steep twisty turns on hills. Although New Zealand roads are pretty good and you do get a great view going over the hills.
Over the Port Hills along Dyers Pass Road past the Sign of the Takahe
Via the seaside suburb of Sumner, over Evans Pass and the Sumner road. This route is an alternative to the road tunnel if you are already on the southeast side of the Estuary.
Via Gebbies Pass, though this is a rather indirect route and is probably only a practical alternative if southwest of Christchurch.
On foot
Walk the Bridal Path from Heathcote.
By bus
Take the number 28 bus from the Bus Exchange to Rapaki/Lyttelton.