To make homemade pickled onions, in a lidded jar, dissolve 1/2 teaspoon sugar and 1/2 teaspoon salt in 3/4 cup vinegar, and bring 2 to 3 cups of water to a boil in a kettle. Cut 1 red onion into 1/4 inch slices, place the onion slices in a sieve, place the sieve in the sink, and pour the boiling water over the onion. Add the onion slices to the vinegar mixture, and stir well before storing in the refrigerator.
Another option is to place 1 cup warm water, 1/2 cup apple cider vinegar, 1 tablespoon sugar and 1 1/4 teaspoons Kosher salt in a bowl. Stir the ingredients until the sugar and salt dissolve, and pour the mixture over 1 thinly sliced red onion. Allow the mixture to remain at room temperature for at least one hour before serving or refrigerating.
To pickle pearl onions, boil 1 1/4 pounds peeled, trimmed pearl onions in water for 4 minutes, and drain the onions. After the onions cool, pack them into sterilized jars with 2 cloves, 1/4 teaspoon mustard seed 2 strips lemon zest per jar.
In a saucepan, bring 1 1/4 cups water, 1 1/4 cups white vinegar, 3 tablespoons sugar and 2 teaspoons kosher salt to a boil to dissolve the sugar, and ladle the hot vinegar mixture over the onions. Seal the jars, and store the onions in the refrigerator.