In article , Martin Brown
writes

You can only do this by attrition. Regular hoeing is as good a way as
any and preventing any seed heads on existing weeds. You cannot do much
about all the wind blown seeds arriving in vast numbers..


The other possible approach is to have a "permanent" mulch of cardboard
with a few inches of straw over it. As the cardboard gets older, rain
soaks through it - but it keeps most moisture in the ground and keeps
the surface soil at a steady temporature. You'd need to temporarily
lift it to get new plants in (and growing from seed would be difficult.
However, this significantly reduces weeds and the amount of watering
required. As a bonus, it makes an excellent environment for various
predator insects - thus potentially reducing pests.

--
regards andyw