I haven’t read the answers above, so forgive me if I’m being repetitive.
I worked for years at two different lawn care companies, and here are some things I learned along the way:
In the long term:
The very best defense against weeds is to have a lush, dense lawn full of grass. Aerate your yard and over-seed it w/ grass seed. Make sure you keep it watered until it has a good hold. Continue to seed the yard in spring and/or fall, every year until the yard is dense with grass. It’s important to use the right seed for your conditions, and your local cooperative extension agent should be able to tell you what to choose. Use a slow-release, balanced, organic fertilizer in the spring and fall. Proper mowing is vital! Keep your blade sharp and set at 3 to 3½ inches, don’t mow wet grass, cut no more than ⅓ of the grass blade off at a time, and leave the clippings on the lawn as often as you can stand it.
In the short term:
I’m afraid that there is no effective organic weed control yet. If you have a yard full of dandelions, your best bet is to let a lawn care company come out and do a blanket application or two of liquid weed control. The good news is that once the product is dry, it can’t be rubbed off or washed off. At that point, it is in the plant. Barring allergies or extreme chemical sensitivity, it’s fine for children and pets once it’s dry. On a hot day, that could take as few as 20 minutes. If the dandelion problem is less severe, any responsible lawn care company won’t do a blanket application, and will spray only the weeds that exist instead of the whole lawn.
As for grubs, it depends on the extent of the infestation and the timing of the treatment. Again, your local cooperative extension agent should be able to direct you. While talking with them, ask about the soil in your area, and what amendments might be needed to improve it. Lime or sulfur are probably the most common, to adjust the pH level one way or another.