To tap your local sycamores you'll need a portable drill (either cordless or a classic brace & bit), a 7/16-inch drill bit, some ½-inch vinyl tubing, and some clean containers to catch the sap. Plastic drinking water jugs are fine, but I've started using plastic vinegar jugs, which have thicker, stronger walls and shouldn't burst due to freeze expansion if your area suffers a cold snap. The sap is just starting to run now where I live in Virginia, and points further south should be well into sugaring season, which lasts about one month.
Once you've located a stand of sycamores, drill a hole about three inches deep on the south side of each tree. Angle your bit upward as you drill. This encourages the sap to drain quickly. Large trees can hold multiple taps, but they might not be as productive. I tend to favor trees about a foot wide. Clean out each drill hole with a twig to remove any wood shavings. Insert one end of the tubing into the hole and the other tube end into your container. Sap flows best on days that are above freezing following nights during which the temp dropped below freezing. Collect your sap each day to avoid overflowing containers. You'll need ten gallons of sap to make one quart of syrup. If that sounds like a lot, don't worry. Each productive tree can yield one gallon of sap per day at the height of the sap run. That means with ten taps you can produce a quart of syrup every day, and 20-25 quarts of syrup over the sugaring season. Sycamore sap can be blended with other tree sap, like maple, birch, and hickory.