Kanji Introdction and Names

Officially there are about ten thousand kanji. Elementary students learn a thousand and six. You'll need more to understand written Japanese.
Kanji are simplified drawings of their meanings based on Chinese. They have changed over the years so that now they are only loosely connected. Meaning can be derived from appearance but reading requires furigana or context.
Kanji have two types of readings (pronunciations): the Japanese on reading used in names, simple nouns, adjectives and verbs (usually one kanji and many hiragana) and the Chinese kun reading for complex words (two or more kanji in a row).

I'll start with names. Many of these kanji are also common in everyday speech and usually a name is two kanji (usually four kana).
As stated above, use the kun reading (and many name specific kanji only have kun readings).
Bewear, the Japanese use euphonics in names. Sometimes in a name where a consonant has already appeared, or where it would be a little difficult to pronounce, they add " to the hard-to-pronounce kana. Hence kawa 川 and ta 田 are often pronounced gawa and da.
Most names are written with simple kanji, but there are also very complex kanji used only in names.
Also, remember that Japanese family names come before their given names, but they understand this is opposite as in the West.