You've got some great advice here already. I'm going into my ninth year of vegetable gardening now and
still have stuff to learn, but here's what I can add:
Make compost. It can be simple and reduces what you put out to trash. I have to ammend my soil a lot because we have naturally heavy red clay, but after several years of adding compost the soil is nice and dark and crumbly. All summer I mulch the garden with grass clippings, they dry in a day or two and looks like straw, I replenish steadily as it decays into the soil. Reduces watering a lot, because moisture is held in. I wait to mulch until the plants are bigger though (not seedling size) because the slugs do live under the mulch and then chomp the tender plants.
I bait slugs with cheap beer- poured into empty catfood cans set in a hollow in the soil- and just pour them out into the trash in mornings. Go out at night w/a flashlight to see what pests are on your plants. Go out early in the morning to pick pest insects off the plants- most of them are slowed down by the cold. If you see a tomato hornworm that looks like this, leave it be. The eggs are parasitic wasps that will eat other pests in your garden, and this hornworm will die while hosting them.
I have a trick for getting carrots to germinate- sprinkle the seed on the soil and then pour boiling water over the row. It helps the seed casings open. I've had much better success w/carrots since I started doing that. Carrots need loose deep soil, if they run into rocks they get crooked, so that part of the garden I always till well- other areas I am starting to just leave alone, adding compost and mulch on top and letting the worms work it all in.
My last idea: find a seed supplier online that grows the plants for seed production in your state. Then the plants will be conditioned already for your climate. When I get seeds as gifts for my mother who lives in WA I use Uprising Seed, they develop seed in WA. When I buy seed for myself I use Southern Exposure Seed Exchange, because technically I'm in the south. Read catalog descriptions to find varieties that will do well with your soil type, harvesting needs or microclimate.
When it's really hot water your plants early morning or at night so it doesn't evaporate quickly, and water at soil level, don't get all the foliage wet or you can get mildew (at least, I have this problem). A soaker hose can be great (I don't have one yet).
When you get some plants doing well, you can save your own seed and grow them again next year- then you've already got something you know works well in your garden. As long as the seed you bought wasn't hybrid. I've saved my own seed many years now, and have some packets in my fridge still germinate for me after 5+ years.
Sorry if that was overkill info, but I hope some of it helps. I love gardening, probably a bit more than I love keeping an aquarium! You can check out my gardening blog here -look thru the plant list in right column for what I've had experience with- and see if any more ideas might be helpful- I write a lot about my mistakes! (to learn from them):
greenjeane.blogspot.com
Someday I think I'll join a gardening forum, but for some reason it's more fun for me to read/talk about fish and aquascaping online than gardening...
Bump: I wish I could add horse manure to my garden. There are lots of horse farms around here that give truckloads away free. But my husband protests that the smell would bother the neighbors- even if the odor was just for a few days. He won't let me do it