Anti-static brush and Rocket Blower. I also keep some Pec Pads and film cleanig solutions on hand, but the liquid cleaners are more for finger prints, and should not be needed for dust.
These methods are far from 100% effective, so I spend a fair amount of time using the Photoshop "Spot Healing" tool (Content Aware) which I much prefer to the Lightroom version. Occasionally the "Rubber Stamp" tool is more effective than the Spot healing tool. It is rare that I can get away with using Photoshop's Dust and Scratches" tool on the whole image, but it can be a time saver if you can select areas which lack fine detail, especially shadow areas and/or sky where the dust shows up the worst.
I have looked at SRDx software <
this website> but I have not tried it. If it works as promised, it is probably worth $50 / 50 Euro.
EDIT: I just tried out the trial version of the SRDx software (above). Somewhat helpful, but not magic. For some kinds of defects it works pretty good, but almost worthless for others. So a lot of clean up was still needed after running the filter. In some areas it was just as destructive to image detail as Photoshop's Dust and Scratches tool.
Has anyone found anything useful on fungus?