The Lua reference manual and the Programming in Lua books (first edition is available for free online) are a good place to get started with the basics of Lua and becoming familiar with the basic syntax and standard libraries. OpenOS strives to emulate the standard libraries very closely, with a few deviations, such as the mostly missing debug library (for sandboxing reasons). These differences are documented on the wiki.
Non-standard libraries will need to be
required in order to use them in a script. For example:
local component = require("component")
local rs = component.redstone
This will allow you to call all of the functions provided by the redstone component. For example:
rs.setOutput(require("sides").front, 15)
Important: when working in the Lua interpreter, do not use local, as that will make the variables local to a single line of input. Meaning if you were to enter the lines above one after another in the interpreter, the third one would error, telling you that rs is a nil value. Why only on the third line, you ask? Because, for ease of testing, the interpreter tries to load unknown variables as libraries. So even though the assignment to component from the first line would do nothing, the use of component on the second line would cause that library to be loaded and used. Libraries are not automatically used when using Lua scripts to keep memory usage low, because that's a limited resource.
OpenOS provides many custom libraries which can be used for many applications, from controlling and manipulating components attached to the computer, to reference APIs for colors used in bundled redstone control and keyboard keycodes. Custom libraries can be used within a Lua script by using the require() function, as above. Some custom libraries require specific components to work, such as the internet library requiring an internet card. In that particular case it is even being provided by it, i.e. the library will show up once you install an internet card - technically speaking, it is contained on a small, read-only file system on the internet card.