Worry not, it isn't too late to throw down a healthy amount of crops to get you through winter, especially if you keep up and plant a winter garden like we do. June is a great time to direct sow squash, cucumbers, beans, and melons. It's also a great time to throw down a silage tarp on ground that you plan to grow in this winter or next spring. The ground doesn't even need tilling, you can do this directly on sod. The result in a few months will be fully workable soil that hasn't been disturbed by tilling.
For the aforementioned squash, cucumbers, beans, and melons, direct sowing is actually preferred by their root system. You can have a harvest in as little as 50 days with many varieties. Now is also a great time to pick up starts of peppers, eggplant, and tomatoes from your local nursery to put in the ground.
You'll also want to start thinking about fall, because in July, you'll need to start many of your longer game fall crops. Don't sow a succession of squash that takes 90 days to finish if you want to squeeze in brussels sprouts into that spot with enough growing time before winter. Winter growing is a whole other beast, we will get into that in July, but for the time being, just keep crop schedules in mind as you plant.
Things NOT to plant in June without special accommodations include things like lettuce, cabbage, spinach, bok choy, and really just any brassicas. It'll be too big of a challenge to keep them from bolting when the space could be better suited towards in season crops, and the cooler season can be dedicated entirely to plants that love it. If you absolutely must grow these things as we head towards the summer solstice, utilize simple shade cloth in place of row covers.
As June marches on, dragging us through the weeds with it, consider making a few hours a week available to work on winter growing projects. Making cold frames that are ready to go at the first sign of frost can mean the difference in death and thriving on for many crops. Consider cutting 9 gauge wire into 4-6 foot lengths to support row covers, or constructing a small hoop house out of cattle panels and scrap wood.
I know this post talks more of what to *think* about in June rather than what to do, but planning is half of gardening, and believing in the future is the other half. Each season is born in the previous one.