Wash and chop your vegetables, and peel your garlic cloves. You can cut your veggies to the size you prefer: A chunky style or a more minced style with smaller pieces will each work well. Set your vegetables aside for the time being.

Sterilize your jars. I do this by placing them in a clean sink and pouring a large volume of boiling water over them. Alternatively, fill the sink with boiling water and submerge the jars with tongs. Either way, use the tongs to remove the sterilized jars to a clean towel or paper towel on the counter, and let them cool until you can easily handle them with your hands.

Make your salt water brine solution by whisking your salt briskly into your water until fully dissolved. 1.5 Tbsp of salt in 4 cups of water will leave you with about a 3% brine solution. 

Layer your mix of vegetables into your jar however you like. Include your garlic cloves, peppercorns, and bay leaf. Gently press your vegetables down so that there are a couple of inches of headspace (at least one) between the top of the veggies and the top of the jar. 

Pour your salt brine over the vegetables, making sure they are all fully submerged. I generally tap my jar on the counter a couple times to release air bubbles, and use a fork to gently press the veggies down. If you have fermentation weights, those can help.

 Cover your jar with an air lock if you have it, or you can tightly cover with the jar lid, or you can loosely cover with cheesecloth or coffee filters. If you choose to loosely cover, make absolutely certain that all the veggies are submerged under the brine. If you choose the jar lid, you will want to burp the jar daily for the first few days to let out any excess carbon dioxide. 

Place the jar on a plate or shallow bowl and leave on the counter at room temperature (preferably out of direct sunlight) to ferment. By the end of the first couple of days, maybe even sooner, you should see signs of fermentation. Little bubbles will begin to appear in the jar, and you'll most likely smell a mild sour aroma (it should not smell strong or rotten). I find that my giardiniera has been right at the sweet spot after about 5-7 days of fermentation, but this can vary. You can begin tasting after 3-4 days, or leave it for up to two weeks. The taste of the finished product will change with longer fermentation: because the lactic acid bacteria eat the sugars in the vegetables, it will continue to develop a more tart flavor with time.

 When you're satisfied with the flavor, tightly cover your jar of giardiniera and transfer it to the fridge.