I only know one method that removes all of the plants you don't want and none of the plants you do want- mechanical control. Physically remove or damage the unwanted plant until it dies.
That can mean destroying the above ground portion of the plant by cutting or tearing it off, and doing that again and again until the plant is exhausted and dies.
That can also mean pulling the weed out. This is easier after a rain and there are tools that can help you. If you get the entire root the plant will not grow back, and if you leave part behind what grows back will be weaker because of what you took last time.
Either of these methods will require several passes, with the first pass taking much more time than the others. The more frequently you pass over the area the easier each pass will be as well, and it's important to get the plant out of the ground before it sets seeds and starts a new generation. I personally find it relaxing as well.
As a final aside, I want to echo another answer that you may want to consider accepting some of those plants as part of the lawn. Especially clover is very popular in lawns because can outcompete many weeds and improves the soil while it grows, is hardy enough to stay green in dry conditions, and most importantly it is good luck.