Learning kanji: only 2500 to go!

Here is some general information about kanji that is useful if you want to learn to use them.

This might take a while

A high school graduate in Japan knows some 2000 kanji, known as the 'jouyou kanji'. They start learning 80 in the first year of primary school, and the tempo increases over time. This Wikipedia entry lists the primary-school kanji (about 1000), organized by grade.

No kanji is an island

You might wonder why 田, which mean "rice paddy", shows up so much in Japanese texts. Do people really have such a need to talk about rice paddies? They don't, but in combination with other kanji, it means all kinds of related things, such as 'farm', 'peasant', etc. More importantly, it also features heavily in names of places and people.
The point here is that learning individual kanji is just the beginning. It's as least as important to learn kanji phrases. Jisho.org, the online dictionary, has links to kanji phrases for each kanji.

Break it down

All but the most basic kanji consist of various identifiable parts which may or may not have meanings on their own. If they do, that's great, because there's a good chance that the meaning of the part will help you remember the meaning of the whole thing.
For example, knowing that 言 (used in 'iimasu') means 'to say' makes it easier to remember that 話 (used in 'hanashimasu') means 'tale' or 'talk', 記 means 'account' or 'narrative', and 語 (the '-go' in 'eigo', 'doitsugo' etc) means 'language'. And the 言 kanji itself has the shape of 口 in it, which means 'mouth'.
It also means that you can get a (very) vague idea of the meaning of an unknown kanji by examining its parts.

Don't try to read what you see (yet)

Almost every kanji in Japanese has at least 2 readings, which are normally completely different from each other. For example, 日 ('sun' or 'day') can be pronounced 'hi' or 'nichi', depending on context. And, of course, 'hi' can turn into 'bi' in certain sound contexts, such as in 金曜日, 'kinyoubi'.
All of this means that it's really hard to read Japanese out loud, and much easier to try to figure out the meaning by just looking.
The best approach is not to think of kanij as representing sounds: very often, they are pronounced as a single syllable or even letter (e.g.　the 言 in 言います is pronounced 'i').

First things first

With at least 2000 kanji to learn, it's good to know where to start. The best approach is to learn the most often used kanji first. Jisho.org indicates a frequency in newspapers for every kanji, but won't give you a list by frequency. This remains a challenge.

The joy of mnemonics

Learning kanji is hard because there are so many of them, and they very quickly become very complicated to look at. To help you learn, use mnemonics: relationships between a kanji and its meaning(s) which you construct.
Here's an example: the kanji 首 means 'neck'. When I first saw it, I thought it looked like a cartoon face: two eyes at the top, a nose in the middle, and a huge grin at the bottom. 'Face' and 'neck' link together quite easily in my mind, so I remember this kanji with fairly little effort.
Here's the important thing: whether 首 is meant to look like a face or not is completely irrelevant. What's relevant is what I thought when I first saw it and saw its meaning, because that's the most likely thing I'll think when I see it again.
In this case, 'face' and 'neck' are somewhat related, but often, my association and the actual meaning can be miles apart. The trick is to bring them together in your mind, even if that seems like nonsense. E.g. if the kanji reminds you of a banana and it means shop, imagine a shop that sells only bananas.
Cognitive psychology has determined that this kind of memorizing is the best way to remember things. I'm applying it to learning kanji, and I think I'm doing OK.