Weeds are very easily dispersed, so are almost impossible to eradicate completely. A longer lawn, with a dense growth habit helps in outperforming weeds, while an aerated soil is a much better option than a compacted soil.
In saying this, weeds can be transferred on shoes, in manure, with animals, or even the mower. Common weeds such as dandelion, bindii, clover and creeping oxalis are all treatable. Some can be removed by hand but often a weed spray is the preferred and better option.
You need to check the suitability of the product you are using for the weed you are trying to remove. Some are not suitable for different varieties of lawn.