Is Esperanto accepting new root words?
Or is this process done and you can create new words only by combining existing ones?
Zamenhof borrowed and made up the first batch of words. He encouraged people to Esperantize words from their mother tongue if they didn't know a word. So from the beginning, there wasn't a central source of authority for new words. This contrasts with other new languages, such as Klingon, toki pona, Tolkien's Elivish, where the stock of root words is limited by the number of words the inventor published. (Derivational creation of words is pretty much unavoidable, even in isolating languages) This doesn't stop people from creating new words, but coining new root words aren't part of the "game" in those community. This is analogous to the rule about having 52 cards in a standard playing card deck-- you can create a new one, but community standards, existing rules of the game don't encourage it and it doesn't happen in practice.
Now that there are native Esperanto speakers, the language is evolving much like any other natural language. I think there is a language board for Esperanto, I'm not sure if it attempts to create new words (like the French one does) or if it is effective at that.
Esperanto does both. One can introduce a neologism, a new international term. Or by combining existing word parts. Not introducing new words is considered optimal, as it saves in words to know. However the new combination must be understandable, and optimally intuitively formable.
Sometimes the terms exist in parallel, until a concensus crystalizes. Usage, listing in partial dictionaries of communities, communications. There are unfortunately no accelerating, prescriptive institutions. An Akademio de Esperanto is rather conservative.
Originally komput-i meant count as in Geiger counter. Computer got a neologismo komputero†, komputoro†, but nowadays komput-il-o (tool to compute) and komput-i is enlarged to mean compute.
In the early years there was hospital-o and mal-san-ul-ej-o (quite notorious). The term malsanulejo, comparable with the German Krankenhaus*, means literally place (-ej) of persons (-ul) with property sick (mal-san-a), opposite (mal-) of healthy (san). The term malsanulejo can be nicely used as negative example of Esperanto, but in fact is quite popular.
Then there are terms without need for introducing neologisms. Animal related names are a positive example of active language possession.
There are stricter guide lines to a good neologism, as Esperanto serves some (European) language families. - The esperantized spelling should be phonetic, though keep visual similarities. ĝeneral-a = (adj.) general, not ĵenerala (more phonetic). - The term should not already exist as other word, or have several meanings internationally. - The term should not be too similar to existing words.
That's a very interesting question and the answer sheds a light into what makes Esperanto unique.
English is a wide-open language, very free in creating new words and idioms (e.g. "spam," "copasetic," "hang 'em high.") This gives English an openness and freedom, but also makes it hard for people to learn. It can lead to impreciseness and sloppiness.
French, in contrast, has traditionally been more disciplined in its vocabulary. Instead of 17 synonyms for one concept, French might have one or two. As a result, I find that French texts are often easier to read.
In Esperanto, the process of word adoption is out in the open. There is long and often heated discussion about the introduction of new words. People become aware of the implication of creating a new word from existing roots and affixes, versus importing a new word from English.
From what I can tell, there are two different currents of thought. On the one hand, writers like Jorge Camacho want the freedom and expressivity of new borrowings.
On the other hand, people like Claude Piron, Renato Corsetti and Anna Lowenstein argue that it's far better to use the native roots of Esperanto. For one thing, the imported words tend to be from English and Romance languages. This makes the language more European-centric, and harder for speakers of non-European languages. In fact, harder for everybody.
Instead, they recommend using the existing Esperanto roots as much as possible. The Esperanto system is so regular and productive, it's a shame not to take full advantage of it.
Piron's book on the subject: http://homepage.ntlworld.com/edmund.grimley-evans/piron/La_bona_lingvo.html
In http://www.remush.be/tezauro/PIV.xml you'll find In green: the words chosen by Zamenhof in his Universala vortaro In red: the official words later added by the Academy of Esperanto. In black: the words added by individuals, and generally accepted by the community. Between [brackets]: a few examples of words commonly built by users of the language.
According to this Wikipedia article, new words come into the lexicon in a variety of ways, including borrowings, coinages, derivations from existing words, and extensions of meaning of existing words.