The solution is simple. It's actually well documented, but not too easy to find. (I had to dig around -- it didn't come up when I tried a few different Google searches.)

The following code works:

>>> from django.template import Template, Context
>>> from django.conf import settings
>>> settings.configure()
>>> t = Template('My name is {{ my_name }}.')
>>> c = Context({'my_name': 'Daryl Spitzer'})
>>> t.render(c)
u'My name is Daryl Spitzer.'

See the Django documentation (linked above) for a description of some of the settings you may want to define (as keyword arguments to configure).