Hi Kingsley,
Welcome to the forum and the exciting world of radio astronomy!
Although I won't say that CLEAN is the best or only option, it will work for diffuse sources. CLEAN works on the principle that sources are uncorrelated on the sky (which is a good assumption) and so can be treated as a bunch of point sources. For diffuse sources, if an emission component is strong enough to make the PSF arising from it brighter than the RMS noise level, CLEANing should work pretty well. Of course there are plenty of different CLEAN algorithms, and Miriad does image-based cleaning while CASA does uv-based cleaning.
I would first recommend reading some information about how deconvolution works in Miriad:
http://www.atnf.csiro.au/computing/software/miriad/userguide/node109.htmlPlease feel free to ask more questions as you play with your data.