Dandelions are weeds that spread over your lawn with the help a puff of seeds that blow in the wind. Once established, they are not easily pulled out of the ground the way other weeds or plants are. They have root systems that go down several feet. Pulling out dandelions generally takes a more labor-intensive approach if the soil is at all compacted.
Pour vinegar on the dandelions to kill the weeds. The dandelions will take the vinegar down to the roots. The plants are strong, and it might take a few applications to kill them all.
Pull on the dandelion at its base, near the ground. Pull slowly and firmly. If you have rich airy soil or sandy soil, you might be able to pull the weeds up now that the roots are weak. If they feel like they are about to break, stop pulling. You are going to have to pull them out of the ground with a little assistance.
Dig down into the ground to get the entire root system of the dandelion. Pulling from the top isn't always possible. Digging down into the dirt, loosens the soil and helps you remove them more easily. If you don't want to have large holes in the yard, try using a manual post hole digger, which will make a small hole straight down.