Step 1: Find Your Trees
Many other trees other than maples can be used. Pecan trees make a fabulous syrup, but I've heard of people using sweet gum, birch, box elder, among others. Each species will have it's own unique flavor.
Step 2: Add the Spiles
Some large scale producers use hoses and vacuum lines to pull the sap from the tree and to a storage tank, but if you're only tapping a few trees in your backyard, that isn't necessary.
Step 3: Collect Sap
You'll want to store the sap until you have several gallons to work with. I recommend checking the buckets a minimum of once a day, and dumping it into a large food grade container and storing it in a fridge or freezer. It will take a LOT of sap to make a little bit of syrup.
Step 4: Boil It Down
Professionals have a "sugar shack" with a huge, flat vessel for the sap. They build a fire under the vessel to boil it down. I only have 2 trees tapped, so I am not going to that extreme. I use a propane fired turkey fryer. I get about 10 gallons of sap and start boiling. Be aware, if you do this on the stove, this creates a LOT of steam, and you can make every surface in your house sticky. I've even heard of people boiling huge pots inside and water logging the drywall on the ceiling. If you don't have a pot big enough, remember you can continue to dump in more sap as it boils down. Once it starts to thicken, you can bring in the maple concentrate and finish on the stove if you like.
As it boils, the sugar concentrates and begins to caramelize making that dark brown color. As the water boils off, the boiling point of the liquid increases. When the liquid reaches 7 degrees above the boiling point of water in your area (219 degrees F at sea level) it's done. Me, I just boil it until it's thick and tastes good.
Step 5: Finishing/storing
For long term storage, you can pour it into sterilized mason jars and put into a boiling bath canner. Contact your local extension office for times in your area.