There are two aspects to "installing optiboot." The first problem, which is discussed here, involves getting the optiboot firmware into chips, whether the chips have an older version of a bootloader, or are completely blank.
The second problem is configuring the Arduino IDE to support the optiboot-loaded chips. This is easy if you're loading up ATmega328x chips, since any 328 chip with optiboot is essentially an Arduino Uno, and you can use the existing Uno configuration. It is more difficult (and not yet documented) if you're adding a new chip, or putting optiboot on a chip that normally uses a different bootloader. This is (will be) described at AddingOptibootChipsToIde.
Much information about burning optiboot into ATmega chips for use in Arduino can be found in the Arduino forums, especially in this thread
There are about three main methods of installing optiboot on an otherwise blank AVR chip.
The Optiboot project here includes ONLY the bootloader, not any support for a chip or chip options in the "core" Arduino code. It also includes bootloaders for many chips, of which only a few are likely to be of interest to any one person. This means that while it is possible to "install" Optiboot in the IDE, this is no longer the preferred way to do thing.
In recent years, since the introduction of installable 3rd party hardware in Arduino 1.6.4, open-source developers have been busy creating additional "boards" for the IDE that can be installed very easily. Many of these cores use Optiboot, or a modified version of Optiboot, as their bootloader, and the preferred method of installing "XXX processor with Optiboot bootloader" is to ignore this repository entirely, find a core for that processor, and use the board manager to install it.
Here are some of the well-known and well-used "cores" that use Optiboot:
If you are using a chip that is "supported" by the Arduino team, or by some other person who has provided files, you can install optiboot (or for that matter, any other bootloader) directly from the Arduino IDE. This usually has the following steps:
There are a couple of Arduino sketches that have been written to make it easier to reprogram Optiboot (or other SW) into other Arduinos, especially in bulk. One example is WestfW's OptiLoader. Similar programs are available from Adafruit and Nick Gammon. These typically contain a pre-loaded copy of some version of the bootloader for several different chips (OptiLoader supports ATmega8, ATmega168, ATmega328P, and ATmega328.) It's very fast and easy IF you have one of the supported targets:
We might assume that you're here at the optiboot code repository because you want to use optiboot on a chip that is NOT supported by another party, but is supposed to be supported by the optiboot in general. (An example might be the ATmega1280, which normally runs a different bootloader.)