Before you even install the countertop that the undermount sink will be installed into, make sure the cabinet is securely in position. The cabinet should be secured to the kitchen walls and level. The size of your countertop and the depth of your cabinets can determine the size sink you can use.
You can choose the amount of work that you need to put into the actual installation of the undermount sink. You can choose a sink model that includes a template along with its mounting instructions. Use this template to mark the cutout location on the countertop, then cut the hole for the sink yourself. Or, you can choose a precut countertop, which is already cut by the manufacturer to fit the undermount sink.
To avoid future leaks between the undermount sink and the underside of the counter, make sure you install the right adhesive, as specified by the sink manufacturer. Usually, you use a silicone caulk, which you can apply either to the sink's flat lip that touches up against the counter underside, or directly around the perimeter of the sink hole on the counter's dust-free underside. For stone countertops, use either silicone caulk or a high-strength epoxy. In addition to this, often you will install mounting screws or clips to the sink and the underside of the counter to keep the sink properly attached underneath the counter op.
Also, you can save yourself a bit of possible frustration if you install the faucet in the countertop and drain to the sink before you actually mount the countertop, along with the sink, on top of the kitchen cabinet. By doing this beforehand, you save yourself the difficulty of manuevering around within the cabinet behind and underneath the sink to hook up these components. Wait to connect water supply lines and install any drainpipes or disposal on the sink itself until the epoxy has thoroughly dried, at least 24 hours.