By car
Cars are not allowed within Matheran. However you can drive up and park your car at Dasturi car point, or take the newly introduced mini bus shuttle from Karjat or Neral railway stations upto Dasturi. From Dasturi you must take a 40 minute horseback or man-pulled rickshaw ride to Matheran along a mud track.
Alternately you can walk from Dasturi along the rail line & make your way up to Matheran - 20minutes to half an hour. The rail track route is slightly shorter, more scenic and very much more comfortable than than the rubbly, dusty main road route. Coolies or porters are available at Dasturi to carry your luggage. Remember to negotiate rates in advance. You can also go with group booking or alone.
On foot
There are several walking trails which ascend the Matheran Plateau. These are used by local people commuting to the hill station as well as the occasional intrepid holiday-maker.
From the Eastern side, trekkers start at Neral see above.
You can also approach from the Western side, which has the distinct advantage that you can be in the shade for most of the ascent if you start early in the morning. One route recommended during monsoon starts from the village of Dudhoni and brings you to Sunset Point in Matheran. It is suitable for beginners, and the ascent only takes 2 hours or so. There is apparently a side trip to a waterfall, but I have not done this. Dudhoni can be reached by autorickshaw from Panvel accessible by bus or central line train. The trail is obvious in most places; when in doubt, ask a local.