Answer: There are a couple of ways to renovate your lawn. You can rototill it up and start all over, or you can rent a core aerator and aerate your lawn, then spread some sand or compost over the area and reseed.
If you decide to redo the entire lawn, start by rototilling the area to break up the soil. Remove any debris (stones, sticks, weeds, etc.) and then spread 4-5 inches of organic matter over the area and rototill it in, then rake the area smooth. Sod produces an almost instant lawn because the grass is mature with a healthy root system. After laying the sod and watering it down well, it only takes a week or two to become firmly established. Seeding takes a little longer, but the results are eventually the same - a lush, thick, healthy lawn. If you decide to seed your lawn, choose a mixture of perennial ryegrass, creeping fescues and bluegrass. This mixture contains both cool season and warm season grasses and will ensure your lawn remains green all summer and winter long.
The second option is to aerate your existing lawn. A core aerator will remove one inch by three inch plugs from the lawn. Leave the plugs on the lawn and they will dissolve in rain or water from the sprinklers. After aerating spread a thin layer of sand or compost over the area and water it in well. The sand or compost plus the soil from the plugs will work their way down into the holes left by the plugs. You can then overseed your entire lawn.
Either approach should improve the soil beneath the lawn and help your lawn grow lush and thick, which will help crowd out any future weeds.
As for fast-growing vines, my favorite is Bignonia capreolata 'Tangerine Dream'. It grows beautifully in the Bay Area, is hardy enough for your conditions, is evergreen, and when in full bloom is absolutely spectacular.
Or, consider Night jessamine (Cestrum nocturnum). In summer, clusters of creamy white flowers yield a sweet fragrance most noticeable at night. While technically a shrub, it has long stems. Plant this fast-growing evergreen in part shade in a warm spot. (It freezes back in heavy frost, but usually recovers.) Unless pruned consistently, night jessamine gets rangy; after flowering, cut it back heavily. Nip regularly to induce bushiness.
Wisteria is always a favorite and while it takes a year or so to establish, once it does, it grows with great abandon.
Best wishes with your garden.
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