Weeds and weeding are perennial battles; even when the weeds are not perennial it feels like they are. So, what is a weed? There is a dictionary definition for 'weed' but it is not necessarily accurate or applicable in all locations. For example; Purslane in my garden is a nasty weed and yet it is cultivated in other parts of the world as an edible and nutritious plant. One year I planted Calendula and found out how prolific it is. It became a weed in my yard. In a broad sense, a weed is an unwanted plant that invites itself to the garden.
I don't think it is possible to eliminate weeds entirely, but with persistence and some caution we can come close. The persistence part is obvious, but the caution may not be. Adding foreign soil to your garden can introduce more or even new weeds you were not anticipating. Adding mature weeds to your compost pile preserves the seeds for distribution along with the compost. Fresh manure can also carry seeds just waiting for their chance. Birds, wind and some water sources also help weeds find their way into the yard.
The persistence part of weed control is primarily cultivation; not giving them a chance to grow beyond germination and propagation.
Weeds appear and reappear every year, but not all of them are actually perennial. Knowing the difference is important for an effective battle plan. Annual weeds die over the winter; their seeds germinate the following spring. Most weed seeds, whether annual or perennial, can lay dormant in the soil for many years. For this reason weeds should never be allowed to flower and reach maturity. Continuous and regular cultivation kills germinating seeds and brings others to the ideal depth for germination. Persistent cultivation eventually brings weeds under control, more or less. If you're not opposed to chemicals, pre-emergents like Preen are also effective on annual (and perennial) weed seeds.
Perennial weeds are largely unaffected by cultivation unless you're able to remove the entire root system. It is still important to cultivate because perennial weeds also develop and distribute seeds. Very often chemicals are the best practical way of battling perennial weeds.
A couple examples of annual weeds: Purslane Crab Grass These are particularly prolific. A single plant allowed to go to seed can deposit hundreds, if not thousands of seeds. Other invasive grasses are often generically called Crab Grass. Crab Grass has a defense method similar to many other weeds. If you try to pull it, it will break off, leaving the roots anchored in the soil. Within days new growth appears with seed heads developing.
Perennial weeds: Field Bind Weed (AKA Morning Glory) is especially tenacious with a root system as much as 15+ feet straight down. Simple cultivation will not kill it but it is still important as it will kill new seedlings. The two-leaf seedling root is about 3 inches long and easily taken out. By the time the seedling develops secondary leaves, the root can already be 10 to 12 inches. Unless you're very particular about your lawn, you don't need to worry about Bind Weed in the grass. Continuous mowing keeps it from becoming overgrown and unsightly. In garden areas I have found success by pulling and/or chopping it out during the spring and summer. Around August I let it grow and then spray it in late September (which means sacrificing bedding plants at the end of their season). Being a true perennial, it is taking its strength into its roots for winter storage. Late spraying maximizes the effectiveness on the entire root. Any broad leaf herbicide will work. I like to use 2-4D
A few more perennial weeds: Couch Grass Mallow Dandelion Mature Mallow and Dandelion have large, heavy roots that must be removed to kill the plant. In early spring, when the Tulips and Daffodils are blooming, I use a narrow trenching shovel to uproot the Dandelion and Mallow in garden areas. The new seedlings are easy to control with cultivation. When these plants become a problem in the lawn, 2-4D is very effective as it does not harm the grass. Couch Grass is very hardy and invasive. Its needle point rhizomes can penetrate potatoes and other semi solid objects. When chopping or pulling the grass, if a small piece of the rhizome is left in the soil it will sprout and spread. Spraying is the most effective way to control Couch Grass which means that if it gets into the lawn, that section of grass will die and have to be replanted.
Weed control is a battle that can be won. Cultivation is the best all around method of control. Soil condition makes cultivating either a chore or a pleasure. The better the soil, the better your tools perform. Cultivating time is relaxing and a time of bonding with the garden.