How can I tell if a word is Sino-Japanese (漢語), or Yamato (和語)?
An answer to How 「えい」 should be pronounced in the words like 英語, 先生, etc? talks about the pronunciation of Sino-Japanese words and Yamato words.
For example, how could I tell whether 先生 was Sino-Japanese or Yamato?
This question could probably be answered on different levels, but here is what you might want to know for starters because that is what I, an average Japanese-speaker, know.
The key word here is phonetics, not orthography.
[大和言葉]{やまとことば} are the words that existed when Japanese was only a spoken language. Sounds were everything we had to express ourselves with, which is why they are still of utmost importance when discussing 大和言葉 even today.
Many 大和言葉, however, are now written using kanji as you know; therefore, using orthography as a key word to answer this question would be straining at best. For instance, 「さみだれ」, as you could tell (or could you?) from its sounds, is a 100% Japanese word with no Sino influence、but because it is usually written in ateji as 「五月雨」, some learners might falsely believe that we borrowed this word from Chinese.
Ateji: http://en.wikipedia.org/wiki/Ateji
Looking back on my elementary and junior high school years, I remember multiple teachers telling us kids that originally-Japanese words consisted of 「やわらかい[音]{おと} = "soft sounds"」 and Sino-loanwords consisted of 「かたい[感]{かん}じの音 = "hard kind of sounds"」.
"Soft sounds" would roughly refer to the "kun-sounds": やまと、さくら、はなす、そら、やま, etc.
"Hard sounds" is, for the Japanese, synonymous to "on-sounds": shin, kin, kon, gan, dan, chou, man, gen, etc. If a word consists of these types of syllables, the chances are it is a Sino-loanword. I will discuss the exceptions later on.
Having never studied Japanese as a foreign language, I have no idea those actually sound "soft" or "hard" to you. It might depend on what your first language is.
Exceptions:
There exist a group of words that are of Japanese origin but are pronounced entirely with on-sounds (hard sounds) as if they were Sino-loanwords. 「[和製漢語]{わせいかんご}」 is what those are called -- literally, "Japanese-made Chinese words".
These include very common (and important) words such as [文化]{ぶんか} = "culture"、[経済]{けいざい} = "economics"、[科学]{かがく} = "science"、etc.
See a longer list here: http://ja.wikipedia.org/wiki/%E5%92%8C%E8%A3%BD%E6%BC%A2%E8%AA%9E
Unless you want to teach Japanese to its native speakers, you would not need to know that these words were created by the Japanese.
An interesting phenomenon is that these "originally-Japanese words" are treated exactly like Sino-loanwords in that these are given the higher, more formal and/or technical word status that we have long given to the Sino-loanwords over our own. Once again, it is the phonetics. Japanese ears are culturally trained in such a way that words that sound "Chinese" are of a higher status and that is precisely how we will treat the words regardless of their true origin.
I've studied Chinese way more than Japanese, so my knowledge probably has a lot of gaps. However, I think the biggest hint in telling if a word is Sino-Japanese (which are mostly nouns) or Yamato is whether the word comes with or without hiragana and whether or not the word is composed of multiple kanji or not.
This isn't a perfect test but it works in many cases: 食べる = Yamato because it has the hiragana at the end 食事 = Sino-Japanese because it's a two word compound
Here's a case where it fails: 大人 you might think is daijin, but it's actually otona.
So this isn't a 100% for sure filter, but it often works.
