June is a great month for the garden. By now, your early planting should start to come into production. I've already been harvesting lettuce and radishes, and kale. My early peas are flowering, and I should have snap peas next week- all those things look really good.
Be sure you keep them well-watered as the temperatures increase. You may also want to apply some shade. I'm putting mine up this week as my lettuce is showing a little bit of stress due to the bright sunshine in the warmer temperatures. That shade will help keep the temperature down a little bit, and conserve some water and make those greens more productive.
Now is also a good time to supply some much-needed nitrogen fertilizer to your growing tomatoes, peppers, squash, and to those existing brassicas.
Generally, I would apply about one teaspoon of nitrogen per 10 square feet over the next three to four weeks. Make sure that gets watered in with that nitrogen will ensure good growth. Don't over-fertilize as this encourages lots of leaf growth and delays the flowering time, particularly in tomatoes and peppers.
Keep up with your weeding and adjust your watering as the temperatures also increase. It's better to water less frequently but add more water than to water daily. Deep watering is the key. This year as we have drought stress, put some mulch around those plants. If you're trimming your grass, put some of the grass trimmings around the base of the mulch to help keep that soil from drying out.
It's not too late to plan a second or third crop of corn and beans. They should be planted until early July plant about every 10 days, and then you'll have lots of good veggies for later in September.