Installing a new shower drain is a fairly simple process to understand. The goal of your drainage system is to get the water flowing to and down the drain. The key components in accomplishing this are the shower collector or pan with three to four inch walls around the side of it. The pan is the non-slip surface at the bottom of the shower that is slightly inclined toward the drain.
It is possible to build your own pan, but it can be very difficult and time-consuming to get the sloping correct and make sure it is waterproof. Therefore, it is much easier to purchase a precast pan. It is also a good idea to use a pan that has the drain located in the same spot as the original collector. Moving drain pipes will involve cutting back or lengthening pipe and will likely require you to rip up a large portion of the floor.
If the drain is lined up, the hookup is simple. The drainage pipe should be facing up toward the collector (it is usually shaped like a "U" to keep stale odor from coming back up the drain). To connect them, you must create a watertight connection between the drain cap on the top of the pan and the drainage pipe. This is achieved by putting a coupling piece on the top of the drainage pipe, then covering it with gaskets and screwing it directly into the drain cap (which acts as a locknut).
In order to get your drain cap to fit into a watertight position in the collector, back off the drain cap once you are sure everything fits together and put plumber's putty around the underside of the cap before screwing it back on. This will create a tight seal between the drain cap and the collector, which keeps water from leaking under it and into the framing beneath the shower.
This is a general guide as the pan you purchase might have more specific instructions. Make sure you check your work with those to ensure your shower drains properly.