Without weeds we'd be out of a job. Please do not let the following information confuse you or put you off. The common weeds are very common and easily pointed out to beginners.
We use hand tools to chip out weeds, or to cut-and-paint woody weed stems with Glyphosate. This is at the handler's own discretion. No sprays are used during working bees. The Brisbane City Council takes care of large and difficult weeding jobs.
Weeds arrive by all the usual means plus flooding. Our worst weeds are all vines and the recently arrived South American, Dyschoristie depressa (no common name but "Rat Plant" would be good).
Dyschoristie depressa fills almost all ground level niches not occupied by something else (and it doesn't mind sharing). It covers broad areas using runners, scrambles up trees and even lives happily under water for at least 4 days (flood observation).
Vines smother and kill. We give no free pass to Anredera cordifolia (Madiera Vine) and will drop everything to eradicate outbreaks. This is not to discount the old enemies of Asparagus sps. (Climbing Asparagus etc), and the various Morning Glory vines.
Firm green stems up to a meter high: Ageratum houstonianum (Blue Billygoat Weed), Bidens pilosa (Cobbler's pegs), and Rivina humilis (Coral Berry) are repeat offenders but do not seem to be as troubling as the Dyschoristie depressa.
Soft stem ground huggers: Commelina benghalensis (Hairy Commelina) from tropical Africa and Asia is very similar to the blue flowering, native Commelina diffusa (Native Wandering Jew) but rather more robust. The white flowering Tradescantia fluminensis, another South American, looks like a white flowering Commelina. We have a couple of patches of Callisia repens (Creeping Inch Plant) and wonder whenever we will get that out totally. When the ground is wet it can be raked out with a metal rake.
Grasses and sedges are confusing at times; there are lovely and very useful native grasses and sedges, but common "foreign" grasses are on our hit-list.
Weed Disposal: We are lucky to have several bays on site where we can dispose of our weeds. Anredera cordifolia (Madiera Vine) is the one thing that we always take off site for disposal.