Hoe off or hand weed seedlings when small. Better still, try to remove dead flower heads regularly to prevent seed dispersal. Other garden plants that can become prolific self-seeders include Anemanthele lessoniana, camassia, chives, fennel (Foeniculum vulgare), Nectaroscordum siculum, sisyrinchium and Verbena bonariensis.
Digging out unwanted plants may work for a while, but is only likely to be a temporary solution. Suppression under black plastic or weed membranes is an alternative but again could take several growing seasons to be effective.
Beware putting invasive plants and their seedheads on the compost heap, as this is unlikely to reach a high enough temperature to kill off seeds, tough roots or underground stems (it is all right if they have already been killed off with a weedkiller). Instead, place them in the municipal green waste, as this is composted on an industrial scale, where tough weeds should be killed off. Burning may also be appropriate, but check your local Council guidelines.
For herbaceous weeds, try a programme of spraying using a systemic herbicide containing glyphosate – Roundup and Bayer Garden Rootkill are common brand names of such products. For woodier plants, choose triclopyr (SBK Brushwood Killer) or glyphosate formulated for stump killing (e.g. Deep Root Ultra Tree Stump & Weedkiller).
Inclusion of a weedkiller product does not indicate a recommendation or endorsement by the RHS. It is a list of products currently available to the home gardener.
Weedkillers for gardeners (Adobe Acrobat pdf document outlining weedkillers available to gardeners; see sections 1a and 4)
Chemicals: using spot and broad-scale weedkillers
Chemicals: using a sprayer
Chemicals: using safely and effectively
Weeds: non-chemical control