I have two leather girths, For these I simply apply saddle soap like I would a saddle and bridle. I have three fleece girths, For these I simply throw in the washer (cold, low spin) and then let them sit dry. I also have a professional's choice girth and this I simply wet a rag and wipe off the dirt, sweat and grime or I rinse it off with a hose.
Hope this helped,
No leather girths in the washer, those you can wash like you would saddles or bridles. For fleece girths I use a stain remover and wash with a non-irritant soap on cold. Air dry and once it has dried I take a dog brush and brush the fleece till its fluffy C: