Yesterday I outlined the ground-penetrating radar technique for finding lava tubes on the Moon. Another two methods have been suggested [1], and I will briefly describe them.
Firstly, seismic survey. This involves deploying a network of seismic sensors (geophones) in the area you wish to search for lava tubes; essentially, microphones embedded in the ground. Then you send shock waves through the ground, like a miniature earthquake. You can generate the vibrations either by explosive charges, or by impacts (i.e. crashing something into the ground from orbit).
Although seismic survey provides excellent resolution and good penetration of the surface, there are problems: you have to non-destructively land your sensors and then embed them. That limits you to a small area. If you're using explosives, you need to set them up as well, or if you're chucking stuff from orbit you need to have some sort of accurate delivery system. To generate good data, you need to have lots of sensors and lots of shock waves from different places. I think that this technique would be good for mapping an area you've already identified as interesting.
The final method is still theoretical, and combines the ideas of GPR and seismic survey. You lob devices from orbit - devices that, when they hit the Moon's surface, behave a bit like EMP bombs, converting their kinetic energy into a very powerful radar pulse. The radar pulse bounces off features in the Moon - such as lava tubes - and the reflections are detected by a very long baseline array of receivers, and converted into 3D geographical data.
References:
[1] D. Stephenson et al., 'lunar resources/lava tubes', sci.space.policy, 22-01-1996
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