Two of the most common nuisance weeds are clover and bindii.
Lawns: to remove clover from your lawn, mow and then fertilise. Lawns love nitrogen but clover hates it, so use an NPK fertiliser which has high levels of nitrogen, phosphorous and potassium.
Garden beds: pull out the weeds by hand and make sure you get the roots. Then, lay mulch in your garden bed to supress regrowth.
If you have a small lawn area, then hand removal is the best option. It's important to make sure you remove the plant along with its roots. Spring is best time to remove it, before the flowers turn into seeds and your lawn is littered with painful prickles.
Weeding is one garden job that is never finished, so the easiest way to keep it under control is to get someone else to do it for you! Your local gardening expert will be able to diagnose your weed problem and offer a solution.