But if you look at the geo_interface protocol (a python object property that returns a geojson dictionary, look at Python Geo_interface applications):
print geom.ExportToJson()
{ "type": "Polygon", "coordinates": [ [ [ 1149490.109727980103344, 691044.609108003089204 ], [ 1191579.109752570046112, 691044.609108003089204 ], [ 1191579.109752570046112, 648030.576115839648992 ], [ 1149490.109727980103344, 648030.576115839648992 ], [ 1149490.109727980103344, 691044.609108003089204 ] ], [ [ 1154115.274565846892074, 686419.444270136067644 ], [ 1154115.274565846892074, 653118.257437493419275 ], [ 1165678.186660513980314, 653118.257437493419275 ], [ 1165678.186660513980314, 686419.444270136067644 ], [ 1154115.274565846892074, 686419.444270136067644 ] ] ] }
it is easier with fiona (also based on GDAL/OGR)
import fiona
layer = fiona.open("myshape.shp")
feat = layer.next()
print feat
{'geometry': {'type': 'Polygon', 'coordinates': [[(1149490.1097279801, 691044.60910800309), (1191579.10975257, 691044.60910800309), (1191579.10975257, 648030.57611583965), (1149490.1097279801, 648030.57611583965), (1149490.1097279801, 691044.60910800309)], [(1154115.2745658469, 686419.44427013607), (1154115.2745658469, 653118.25743749342), (1165678.186660514, 653118.25743749342), (1165678.186660514, 686419.44427013607), (1154115.2745658469, 686419.44427013607)]]}, 'type': 'Feature', 'id': '0', 'properties': OrderedDict([(u'FID', 0.0)])}
print feat['geometry']['type'])
Polygon
print len(feat['geometry']['coordinates']
2
# outer ring
print feat['geometry']['coordinates'][0]
[(1149490.1097279801, 691044.60910800309), (1191579.10975257, 691044.60910800309), (1191579.10975257, 648030.57611583965), (1149490.1097279801, 648030.57611583965), (1149490.1097279801, 691044.60910800309)]
# inner ring
print feat['geometry']['coordinates'][7]feat['geometry']['coordinates'][9]
[(1154115.2745658469, 686419.44427013607), (1154115.2745658469, 653118.25743749342), (1165678.186660514, 653118.25743749342), (1165678.186660514, 686419.44427013607), (1154115.2745658469, 686419.44427013607)]