How to understand the pronunciation of "nod" and "node"?

The "extra e" (or "silent e") at the end of a word is a convention which serves as a sign that the preceding short vowel should be elongated into a long vowel. It was introduced by Richard Mulcaster in 1582 via his book Elementarie wherein he called it a "qualifying e". The Wikipedia article on the "silent e" makes for fascinating reading.

The rule is, however (and as with most aspects of English orthography), inconsistently employed. While node, side, and rate all involve long vowels, words such as love, give, and sieve do not.

Wikipedia has other pages on English spelling that might prove useful to you.