In general, weeds fall into three categories: easy to pull out, deep-rooted and spreading.
The easy ones could be any plant that you think just doesn't belong there. Chickweed, bits of shallow-rooted grass, even self-seeders like forget-me-nots and dame's rocket all fall into this category. You may have dozens but a quick pull or swipe with a knife and they're gone.
Deep-rooted weeds like dandelions are best attacked with a shovel, at least when they're mature. Loosen the soil on one side with the shovel and they'll pull right out. Little ones can be taken out with a knife. Just be sure to get almost all the root or it will sprout up again.
The spreading ones are the tough ones. Some, like buttercups, send out runners over the top of the soil. Others, like quack grass, sheep sorrel and many ground covers spread by underground runners. Taking out the tops is useless, you need to remove every bit of the runner or it may root and start over again.