Wash one heatproof quart size jar or two pint sized jars in warm soapy water, and rinse well.
Place the jars on a rack in a pot large and boil for 10 minutes to sterilize. Keep warm until you are ready to fill.
Wash and cut your vegetables into desired shapes, such as bite-sized pieces, slices, spears, or chunks. Set aside while you make the brine.
Make the pickling brine by combining the apple cider vinegar, water, sugar, pickling salt, and pickling spice in a saucepan. Heat until just boiling, reduce the heat, and simmer until the sugar and salt have dissolved, about 3 minutes.
Remove the jars from the hot water, drain and place on a kitchen towel.
Fill the jars with the prepared vegetables, dill, mustard seeds, and celery seeds.
Pour the hot pickling brine into the jar and cover the vegetables.
Add the lid and let the jar cool to room temperature for about 1 hour.
Label, date, and store the jar in the refrigerator for at least 24 hours to let the flavors infuse. Use within 3 months. Yields about 1 quart or 2 pint sized jars.