There are a range of techniques that range from relatively cheap through to very expensive.
The cheapest option would be to combine a multi-resolution valley bottom flatness algorithm http://onlinelibrary.wiley.com/doi/10.1029/2002WR001426/abstract
applied to SRTM DEM data http://glcf.umd.edu/data/srtm/
to characterise depositional/sedimentary terrain and then do a multi-temporal analysis of either MODIS EVI or NDVI
(annual minimum values work well) to identify areas of persistent greenness. In most water limited environments the areas of persistent greenness are typically those that recieve a degree of groundwater supply (or are supported by anthropogenic irrigation).
These data streams are freely available and will give you good 'first cut' insight into areas of groundwater expression at surface for large expression zones.
If you've got the resources, you can apply a similar multi-temporal approach to Landsat to identify smaller wetlands and GW dependent vegetation communities.
If you've got a LARGE budget then you can always go for airborne (plane or helicopter) borne airborne electromagnetics. However this is a costly solution and the cost lies in both the acquisition AND analysis of the data. Good luck!