Dig them up.
No I'm not being funny, that is the best way without resorting to weed killer etc. Don't rotovate it either - that just chops the weeds up into smaller bits and they come back even more then before.
section parts of your garden off to keep the kids and dog out and just glyphosate it out of a watering can.
Roundup.
Spray on a sunny day and keep the kids and pets off until the following day. 2 weeks later all the plants and grass will be dead and ready to rake up.
If you need to find a tradesperson to get your job done, please try our local search below, or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Are you a trade or supplier? You can create your listing free at DIYnot Local