I disagree with nice gaijin and would argue that it is most productive to learn only one reading of a Kanji at a time. For a beginner, for most Kanji, this will be the KUN reading. (By all means make a note of the other reading but don't worry too much) Once one reading is known and you are familiar with the Kanji you can then go back and learn the ON reading a couple of days later, the thought would go: "oh the ON reading for Kanasii is hi, like in higeki" not "OK so the readings for 悲 are kanasii, kanasimu and hi and it means sad" That would be much harder to remember in my opinion.
It is easiest to learn ON readings within a piece of vocabulary, rather than by itself. Its easier to remember the word 電車 than the individual readings for each kanji. Then when you need to know the ON reading for 電, you can think, oh yes, its the den like in densha. However, in order to do this some Kanji already needs to have been built up.
There are cases where its not worth beginners learning the KUN readings too, and the ON is much more valuable.
然る 【しかる】 (adj-pn) a particular, a certain
is not an important word for beginners, but
自然 【しぜん】 (adj-na,adv,n) nature, spontaneous, (P)
is. And there are Kanji with no KUN at all, like DEN above. So the method I mentioned above doesn't always apply.
Difference between ON and KUN:
KUN readings are used when a Kanji is used by itself as a single word.
悲しい かなしい sad
KUN readings are usually unique to that Kanji.
ON readings are used when a Kanji is combined with another to form a single word. Like 悲劇 ひげき tragedy
Many Kanji share the same ON readings, these Kanji often look similar giving a clue to the reading, but also often don't.
eg: 非常 【ひじょう】 (adj-na,n) emergency, extraordinary, unusual, (P)
非 looks like 悲 and both have the ON reading 'hi'. However they have very different meanings.