Start by sterilizing your jar: You'll want to let it come back down to room temperature before you begin filling it. To do this, I place a clean towel on the counter and my jars in a clean sink. Pour boiling water over the jars and use tongs to move them to the towel on the counter.
Cut your cucumbers: You can do slices, spears or leave them whole if you are using gherkins. I do recommend cutting off the "blossom end"- the opposite of the stem- if you are using whole cucumbers. If the blossom end is left on the cucumber it can cause the pickles to be mushy.
Once your cucumbers are cut and the jar is ready to use, you can place the cucumbers and your spices in the jar.
Mix your salt brine: A salt solution of about 5% salt by weight tends to be an excellent amount of salt for taste & for promoting the fermenting process. I do usually calculate my salt by weight in grams: to do this, zero your kitchen scale with your liquid measuing cup on it, then add water to the cup to obtain the weight of the water. Multiply this by .05: for example, 400g water x .05= 20g of salt.
If you prefer to not use the kitchen scale to calculate this, 1 level Tablespoon of kosher salt per 2 cups of water should be about right. The brine solution is more than forgiving enough for you to use this method instead.
Stir the brine until the salt dissolves, then pour it into the jar, making sure the brine covers the top of the cucumbers. Since vegetables tend to like to float a bit, a glass fermentation weight can be really helpful for this. Jiggle or tap the jar on the counter a couple times: You don't want to start out with any air bubbles in the jar at all.
Leave the pickles on the counter, out of direct sunlight, to ferment for about 2-3 days. I recommend sitting the jar in a shallow bowl to catch any overflow of brine. After about a day to a day and a half, you should start seeing some evidence of fermentation: little bubbles will appear at first. Eventually you may see a little layer of foam at the top of the jar as the bubbles make their way up.
After two days or so, if you are seeing signs of fermentation, you can taste your pickles, cover them, and store them in the fridge. Once they are in the fridge, they are ok to no longer be covered by the brine, so if you need to pour off a little to put a regular lid on the jar, that is perfectly fine.