The best things I've found for memorizing kanji for me (personal preferences, YMMV ):
1) If you haven't noticed already, most (if not all) kanji are "built" from the same (rather large) set of predefined strokes. eg. "think/remember" 思 is a combination of "field" 田 over "heart" 心, "section" 課 is "say" 言 next to "result/fruit" 果, which is a "field" 田 over "tree" 木, and so on. I found it a lot easier to make sense of any new kanji I came across if I looked at what parts it combines rather than as a pictograph. Even if you don't know what all the individual pieces mean (for example, for 解, I can only tell you the cow 牛 in the lower-right hand corner at first glance ), recognizing these individual tokens makes for a slightly easier time.
Of course, if you're just starting out, this idea won't help you. This presumes you're been studying for some time - if not, the next points may help more.
2) Details are everything, so observe your kanji carefully for things such as what strokes are longer or which ones stop where or where little dots are. If you're not careful, you might not think there's a difference between 末、天、and 夫. Or 学 and 字 (in a rush, your mind might panic), or one I finally memorized lately - 頂 and 預. Even in hiragana, the difference between は and ほ can be subtle. The basis for distinguishing Chinese characters from each other aren't always the same as Western characters.
3) Don't be afraid to use any particular mnemonics to help you memorize the strokes *and* the meaning. (I stay away from recommending mnemonics that only do one or the other unless someone is *very* good at dissociating as well as associating.) For example, I learned half 半 by thinking of "a dead cow flat on the ground, cut down the middle." (My intro Japanese teacher was an interesting one. ) Being in trouble 困 was "a tree in a box will die over time". The sillier or stranger, the better, as most people tend to remember the unusual better - just make sure it makes sense to you. Trying to learn 回 as "a box in a box repeats itself" can work, but 白 as "a day with a dot turns white" is a lot less likely to stick. And actually, just as I was thinking about this, I managed to come up with silly sentences for a good number of simple kanji. (For some things, there may be no better way than to beat it into your brain, so don't tax yourself trying to be witty.)
4) As for word memorization - studying a whole bunch of words from the same kanji seems intuitive, but I might propose that you instead try studying vocabulary that's semantically similar as opposed to merely on a character basis. I think there've been studies on the way people think about their vocabulary, and when a particular topic or theme comes up, the brain is supposed to "preload" (anticipate) the words it expects to hear or use on that topic. Most of the time, there won't be much difference - same characters, same general stuff - but knowing the way I think about things, I find some words going into different groups. For example, mouth 口 is a body part, which I would probably study with other body parts (頭 head、腕 arm、首 neck、目 eye、鼻 nose...). But 口 also represents entry/exit points （川口 mouth of a river, 出口 exit...), which I would probably separate. Then there's other instances of 口 (辛口 spicy flavor, 口紅 lipstick) which would seem to be better associated elsewhere (for me, 食 food and 化粧品 cosmetics).
Of course, this is only what works for me. Keep working at it and you'll eventually find what strategies work best for you. がんばるのだ！
when learning kanji learn them in groups (verbs, adjectives, foods etc) not as compounds (2 kanji together) because you will start learning advanced kanji mixed with the basic kanji.
When you split a kanji or even have 2 kanji the pictogram idea start losing merit, things like 切手 (pictogram meaning: cut hand, really: postage stamp) will cause trouble. A trick that i use for quickly identifying the readings for intermediate-advanced kanji is to pick out the 'radicals'.
Japanese kanji are made up of little building blocks called radicals. Theres about 215 of the little blighters. The basic kanji are all pretty much radicals, 一 二 力 口 水 乙 日 月 火 牛 田 王 and many more. Once you learn all the easy ones drawing the bigger ones becomes easier if you can pick and draw the smaller radicals. 聖 (sei, prefix meaning 'St' / 'Saint') is 耳 + 口 + 王
...more or less, I think I like Ewok's answers better than mine - much shorter and to the point. (and I completely forgot what a radical was )
Hey first-poster. And yes, a background in Chinese will help immensely (as I understand it, Japanese kanji have their roots in Tang dynasty Chinese). However, modern Chinese has evolved a bit, so having to re-learn a few meanings can be a pain. (eg. in mainland China, 天 is sometimes used to mean a day - tomorrow would be "ming tien" 明天 instead of "ashita" 明日 in Japanese.)
Something I find interesting: one of my Chinese friends has been playing Dynasty Tactics 2 (a Romance of the Three Kingdoms game) completely in Japanese without any help from me. Of course, probably helps that all the people, city, and strategy names are entirely in kanji (eg. 孫策 Sun Ce)