As a general rule, kanji in words that contain hiragana (like natsukashii) use the kunyomi, single kanji often use kunyomi (水 is read mizu and not sui unless you put it in a compound like 温水 and it becomes onsui), and compound kanji words, easily spotted by their lack of hiragana and often found in technical jargon of every kind and proper nouns, use onyomi. As with most languages, this is not a hard and fast rule and there are tons of exceptions. All bets are off when it comes to place names and family names. One example is that 'Sui' goes back to being 'mizu' in the often seen place name and family name Shimizu 清水 despite the fact that it's a kanji compound.
Nitro: regarding your question about suffix, natsukashii is actually the entire word and contains no suffix. The line between hiragana and kanji in a word that contains both does not neccesarily denote prefix/suffix. Instead, the line between a kanji character and hiragana characters will often approximate what will change when you create different conjugations/forms of the verb/adjective/whatever. E.g.: Tanoshii or 楽しい will change to 楽しかった for the past tense, 楽しくない for the negative, 楽しくなくなりました for "it became not fun" and countless other variations. Notice the changes all occur after the し shi after the kanji character. That all may not make any sense.
All this being said, I'm definitely no expert and some of this may be wrong. Lazerbeat would probably be a better person to ask. If you do have other questions though, I'd be happy to try and answer them.
And, yeah, furigana is awesome despite being aesthetically ugly.