Is there some way to derive word from suffixes on the fly, as in, in a conversation? [...] If I don't know a word, can I derive it simply from a list of roots and endings?
Yes and no, but mostly yes: If you have a concept in mind and don't know an Esperanto word for it, you can build one with Esperanto's word building system, that will usually be readily understood. Proficient speakers can (and often do) do this on-the-fly.
the word you come up with for the concept will be a word for the concept, not necessarily the word for the concept. There might already by one or more well-established words (whether basic ones with their own root, or ones also built with the word building system) for what you're trying to express and using them might be considered more correct than what you've just built on-the-fly.
some existing built words traditionally have a meaning that is more specific than what can be determined from their building parts. For example
- mal·san·ul·ej·o can be analyzed as "place or facility (·ej·o) for people or a person (·ul·) who are the opposite of (mal·) healthy (san·a)" but is quite specifically a hospital and not just any generic facility for sick, ill or injured people.
- tranĉ·il·o can be analyzed as "tool (·il·o) for cutting (tranĉ·i)", but is means specifically "knife" and not, e.g., "scissors".
so if you by chance happen to build such a word without knowing it, you might be conveying a meaning more specific or slightly different than you intended.
This quote says that the process for deriving words is regular
It is mostly regular, and probably much more regular than in most national / ethnic languages. But don't take that as it being completely regular also for pre-existing built words. (See examples above.)
how is it done? If I don't know a word, can I derive it simply from a list of roots and endings?
There's roots, prefixes (beginnings), suffixes (endings) and word-type-indicators.
Lernu.net has a whole grammar chapter on the word building system and Duolingo has a "skill" focusing on just that topic. (See here for Duolingo's tipps on the skill.)
You'd usually begin with a root that conveys the base / main meaning of the word. You can attach prefixes before it and suffixes after it (usually removing the word-type indicator before adding a suffix) to alter its meaning. You can combine several such conglomerates to a single word, if appropriate. (Then the last / right-most conglomerate would give the base meaning and the conglomerates prefixed to the left would be modifying it.) Finally, you can attach a new word-type-indicator at the very end.
Let's play that through on the hospital example:
- The topic here is health. san·a means 'healthy', 'of good health'. Let's start with that. (The ·a marks it as an adjective.)
- Prefix mal· turns something into it's opposite, so to express 'sick' / 'ill' we can use mal·san·a.
- The suffix ·ul· indicates a person with that trait. So a healthy person would be a san·ul·o, a sick or ill one a mal·san·ul·o. Note how we removed the ·a and added an ·o, to indicate that these are now nouns.
- The suffix ·ej· indicates a dedicated place or facility for what comes before it. So the hospital can be expressed as mal·san·ul·ej·o. Note that we've removed the final ·o, added ·ej· and then added back a ·o at the very end, because the whole thing is again a noun.
Sometimes the base meaning doesn't have a root of its own, but there's an affix for it. In those cases, one can (ab)use the affix as a root:
- in·o - a female (i.e., a woman or girl, in specific contexts maybe a female animal)
- ej·o - a place for doing something specific, a facility
Sometimes this is also done when a root exists, to gain some brevity or a different nuance:
- mal·o - an opposite (synonym of kontraŭ·o, a contrary)
Does such a list exist?
Any good grammar book and many good dictionaries will contain a complete list of affixes (prefixes and suffixes) and of word-type-indicators. Comprehensive lists of roots might be harder to come by and there might not be an absolutely complete one, as Esperanto allows the addition of new roots for concepts where it's impossible or too impractical to express them with existing roots and the word building system alone.
In PMEG you can find the lists of affixes here.