Some people suggest that a fall crop actually tastes better than a summer crop of cool season plants. There is valid reasoning behind this. Spring-sown plants are encountering stressful conditions at the point they are ready to harvest. The increasing sun and heat affects their growth and taste (see my article, "When Plants Bolt"). Summer-sown plants are able to direct all of their energy into growth and improved taste because the cooler autumn conditions don't trigger bolting and seed development.
To plant a second garden, for fall harvest, you can use the same plots for the same cool season plants. Your spinach still looks good, but it's past the point of usefulness in the kitchen. Pull it out, throw it in the compost pile, and sow new seeds. If you're letting some of the spinach flowers develop into seeds fully, as I am, sow in rows between the old, straggly plants. When you collect the seeds for next year you can pull out the old plants and add them to your pile. The new seedlings will have room to grow.
Either way, the soil needs to be kept moist while the seeds germinate and in summer that may mean extra watering. In spring you can get away with minimal irrigation as seeds develop, but in summer it requires extra effort to ensure the seeds don't dry out at a critical point or that the seedlings don't desiccate in the wind and sun. In return you won't have to water as much in fall because the plants' needs are reduced in the cooler conditions.
Knowing your first frost date is important so you have an idea of how long you have available for the plants to reach maturity and produce a crop. Allow enough time from summer sowing to fall harvest based on your local climate.
Many cool season plants can handle a light freeze so the first frost won't be as devastating for them as for warm season plants like tomatoes and peppers and beans and squash. Broccoli, cauliflower, cilantro, lettuce, peas, spinach, and chard can all shrug off a light frost. Some, like kale, Brussels sprouts, beets, cabbage, and collard greens can survive down to 20F degrees.
You can expect a steady and longer harvest of summer-sown plants. Radishes, carrots, and parsnips can even handle frozen soil. I'm told parsnips actually taste sweeter when allowed to endure freezes into January. That's my harvest plan for this plant new to my garden this year.
With season-extending structures, you can lengthen your fall harvest even more (see my article "Extend Your growing Season with Mini Greenhouses"). Light frost and even killing freezes can be combated by covering your plants.
So don't despair that so much of your garden has stopped producing and is withering. Use the opportunity to continue gardening well into the cold months of the year. Plant in summer for a fall crop that may provide bounty into winter.