When I see a kanji or a word consisting of multiple kanji somewhere, I want to enter them into a computer so that I can search for it and translate it.
Are there any methods or "systems" that allow faster input and search of a kanji? I'm asking about methodology, not any specific tool.
Some sort of auto-complete search, that allows searching for kanji by splitting them into parts or radicals, or something like the SKIP system, which I am currently learning how to use.
The easiest way is for you as a non-native to learn how to use SKIP codes and then use a dictionary that is sorted by SKIP code. http://www.basic-japanese.com/Hilfsdateien/skipCode.html
Even when I went to university in Japan, this was the method they taught non-natives to use. I do not know if that's how the Japanese learn (I don't think so), but that's definitely how they taught us non-Japanese.
There are a few methods you could try, but none with universally perfect results. I'm also not fully sure what you are looking for, so i'll sort my answer to try make it easy to find something that suits you.
Improving accuracy of selection using existing IMEs
For regular Japanese IMEs, quite a few allow you to sort by radical, which are in turn sorted by number of strokes. Mac's IME offers this, as do a few others, though I don't remember if Windows' does (?). This is perhaps the fastest way to search for 漢字 individually. Quite often, though, for finding individual kanji, there is usually a 訓読み{くんよみ} reading that is unique (or mostly unique). Even if it's not correct for the sentence, i sometimes find myself doing this.
Take the example reading "I was thinking of going to Guangzhou":
広州{こうしゅう}へ行こうと思っている
こうしゅう has quite a lot of readings, so you could instead write as 広{ひろ}い州{しゅう} then delete the い. It's a lot faster to type that needing to scour the entire list of kanji compounds read as こうしゅう. It's just a suggestion, but albeit not necessarily the best.
Better keyboards and IMEs
I'm not sure if your complaint applies only to kanji, or to Japanese typing being slow generally. If you're upset about speed of type overall, you could change keyboard altogether. Romaji input works OK, and has a lot of users, but you end up needing to type at least 2 keystrokes for every one Japanese kana, and quite a few more for 漢字, too. The input method I use is the JIS (Japanese Industrial Standard), which assigns each keyboard key to a different kana. It means that the strokes you need to input generally will about halve.
Kanji prediction may not be a whole lot better, but you'll be typing less, and even with the time spent dishing out Kanji, you can still always list by radical as stated in the above section, and cut down your time quite a lot.
Separate Kanji input by Shape
Probably the least popular of all of these methods. Chinese has a few methods of inputting Hanzi (kanji for Chinese) by shape, some of which, including Cangjie and Wubi, will produce virtually no overlap, so that any one key combo applies to only one character. Usually they're not designed for Japanese, but in the case of Cangjie and wubi, they both still store Japanese Shinjitai, so it's possible to use it for Japanese too. These are also the closest thing to the SKIP system, except designed for real input by real users of Chinese characters, so work quite a bit better on the whole.
I sometimes use this, too, because I know Chinese, and took the time to learn Cangjie, and later Wubi too, to input that. For Japanese, they work equally as well, with the only major disappointments being that
It's probably not overall worth using either of these, and the Japanese predictions may be faster just to flip through if you were considering this.
Handwriting
Not the fastest method, but certainly an accurate one. On the mac, the trackpad is the perfect environment to use this type of method for because the trackpad is generally excellent for this type of thing. Windows needs you to use your mouse, and click to put the pen down. A lot less natural, slower, and gives you worse handwriting, but still a possibility. If you're using a mac specifically, I'd recommend this one quite a lot, but otherwise I'd ignore it as a possibility (especially with a mouse, it's a struggle to input characters properly).
Which is fastest?
My experience is that the fastest is using kana input (JIS) if you don't already, and stick it out trying to interpret lists by radical. It cuts down typing time dramatically even for hiragana / katakana, and you can use this as well as kanji lists by radical to try cut down your typing time even more.
If you can't stand switching from romaji, or really just don't like reading lists, you can try download an IME online with better prediction software so that you're less likely to need to scroll through lists in the first place. I sadly haven't found any for Japanese so far, but if you do, please tell me.
