In a medium saucepan combine the garlic, water, vinegar, sugar and salt.
Heat to a boil, stirring to dissolve the sugar and salt. Once at a boil, add the sliced jalapeños pressing them so they are submerged. Remove the pot from the heat and let it sit for 10 to 15 minutes, occasionally stirring and pressing the jalapeños into the brine.
Transfer the jalapeños to 2 pint-size jars or 1 quart-size jar. Ladle the brine over top until the jar is full (doing this over a small strainer will remove the bulk of the excess seeds). Let cool at room temperature before securing a lid and popping them into the fridge.
(Alternatively to can them: when the mixture is still hot, process the jars in a boiling water bath for 10 to 15 minutes; make sure the jars were sterilized first and use best canning practices to ensure food safety; the USDA also has good resources on canning).
Notes
If you already have pint-size Mason jars, you're halfway there. I also prefer plastic lids in place of metal, since I don't process my pickles. I simply store them in the fridge, and the plastic avoids rusting.
I always recommend chilling the jars overnight before enjoying any of the pickles. They will still be very spicy that first day, but the pickling will continue as they chill into the next day.
These homemade pickled jalapenos will last for months in the refrigerator.