For most herbaceous plants, some grasses, and seedling trees and shrubs, pulling plants by hand can be an effective control strategy. Wear gloves to protect your hands and be sure to pull out as much of the root system as possible. Time your hand pulling efforts to occur in the spring or after rain when the soil is moist and loose.
Weed Wrench /Uprooter/Extractigator
There are tools created to help pull small trees and shrubs from the ground. An old model, no longer sold, was called the Weed Wrench. Current versions on the market include the Uprooter or the Extractigator or the Pullerbear. These tools leverage your strength to more easily pull small trees and shrubs from the ground. As with hand pulling, it's important to pull out as much of the root system as possible. These tools will work best when the soil is moist and loose. Bare soil left after pulling could be recolonized by invasive species, so it's a good idea to cover bare patches with leaf litter or plant with native seed.
Some invasive plants can be controlled by cutting/mowing. Frequent cutting/mowing over multiple years will deplete energy stored in the roots of perennial and woody plants, and can kill them. Hand tools like pruners, loppers, and saws can be used to cut invasive plants. Chainsaws, brush cutters, and mowers can also be helpful.
Do NOT mow plants like wild parsnip or garlic mustard when their seeds are mature, as you will spread the seeds. Depending on the species, it may be necessary to bag plant material and burn or dispose in a landfill, because seeds or plants parts may grow new plants. NEVER bring invasive plants to a yard waste site, because they may grow new plants there.
Often, cutting/mowing is used with herbicide to achieve more complete control.
In some cases, infestations can be controlled by smothering. Smothering requires covering an area with cardboard, newspaper, mulch, black plastic, or a combination of materials to block plants underneath from receiving sunlight. Without sun, the plants cannot photosynthesize and may die. For best results, be sure to cover a few feet past the infested area. Monitor the area to make sure that the smothering material stays in place and plants do not sprout outside of the covered area. Plants may survive in a dormant state under the material for months or years, depending on the species. After removing the smothering material, plant native species on the bare soil and continue to monitor for invasive plants.
Weed Wrench in use! Image from https://www.ecolandscaping.org/