There’s probably no limit to the number of possible approaches to building up your vocabulary of kanji. One way that’s definitely helped me acquire more is organizing them into a relational database — so to speak, mixing and matching characters that share common attributes.
To demonstrate how this works, let’s review some of the many characters using 手偏 (tehen, the classifier for hand).
Written 手 and read te or shu, the character for hand itself resembles a stick-figure representation of (in descending order) a thumb, four fingers and a wrist. It belongs to the category of kanji called 象形 (shōkei, pictograms). Classifiers representing parts of the body also include 口 (kuchi/ kō, mouth); 目 (me/moku, eye); 耳 (mimi/ji, ear), 足 (ashi/soku, leg); 髪 (kami/hatsu, hair on the head); 鼻 (hana/bi, nose); 歯 (ha/shi, tooth) and 毛 (ke/mō, hair other than on the head). Be careful with this last one; at first glance it almost looks like a reverse image of the character for hand.
The tehen hand classifier, written 扌, is the simplified form of 手 and is written with three strokes, one less than its standalone kanji form. (Be careful not to confuse it with 牛偏 (ushi-hen, the ox classifier), which it closely resembles; this appears in such characters as 物 (mono, thing) and 特 (toku, special).)
Most, but not all, of the tehen characters have some relationship with actions and activities people do using their hands. Many have been provided with some mnemonic attribute to help in recognizing them. As one example, let’s look at 擽 (raku or kusugu(ru)), meaning to tickle. It’s composed of the hand classifier on the left and a phonetic component, 樂, that can be read as 楽 (raku or tano(shii), meaning “to enjoy or take pleasure”) on the right. This gives us a character meaning “to give pleasure with the hand.”
In another character with a practical mnemonic, the hand classifier is combined with 蚤 (nomi, flea). That gives us 掻く (kaku), as in “to scratch an itch.”
Sometimes the tehen is used in both characters of a compound word, enabling one character to supplement, reinforce or clarify the other. One common example is 把握 (haaku), which, followed by suru, means “to grasp,” usually in the figurative sense. Another is 投げ捨て (nage-sute), made from the verbs nageru (to throw) and suteru (to discard), closely resembling the English “throw away.”
Then there’s 掏摸 (suri, literally, “picking-groping,” i.e., a pickpocket). And also 打撲 (daboku, to hit), from which we get 打撲傷 (dabokushō, a bruise). Note that its second character, when pronounced mō, appears in 相撲 (sumo) — which literally means “mutual bruising.”
In terms of everyday usage, it’s hard to beat 持 (ji or mo(tsu), meaning “to hold”), a character that in ancient times showed the hand classifier on the left and a stylized image of a hand holding an object on the right. It combines with other verbs to give words like 持って帰る (motte–kaeru, to take something home), 持ち込む (mochi-komu, to bring in) and 持ち出す (mochi-dasu, to take out).
It also combines with nouns to form such words as 持主 (mochi-nushi, owner) and 金持ち (kane-mochi, a wealthy person). In its other reading we can find 持病 (jibyō, a chronic disease).
One character that pops up in many different contexts is 接, pronounced setsu and having widely varied meanings. The components on the right side, 妾, would appear to show立, the character for stand, above 女 (onna, woman). However, according to the 漢和辞典 (Kanwa Jiten, Dictionary of Kanji Derivations), the top part was originally 辛 (shin, meaning “hardship”). And in its most ancient form it referred to tattoos applied to women when taken into slavery. Then it evolved so that 妾 came to be read as shō or mekake, meaning “concubine.”
Which brings us back to 接 (setsu), which can be used as a standalone verb, as in 接する (sessuru, to come in contact with or to touch). It also appears in dozens of compound words, such as 接続する (setsuzokusuru, to connect).
In TV weather forecasts you’ll often see 接近 (sekkin, to approach), such as 台風十二号はあっさてより紀伊半島に接近する（Taifū jūnigo wa asatte yori Kii–hantō ni sekkin suru, “Typhoon No. 12 will approach the Kii Peninsula from the day after tomorrow.”）
Another useful word — although it has nearly been supplanted in modern conversation by the English キス (kisu, kiss) — is 接吻 (seppun, literally, “connect lips,” or a kiss). Note how the first of the two characters uses the hand classifier and the second, the mouth classifier, perhaps subtly suggesting the order of how things happen — an embrace followed by a smooch. You’ve really got to concede that writers in ancient times knew what they were doing when they developed kanji!
Back to setsu again, there’s “straight connect” or 直接 (chokusetsu), meaning “direct,” as in 彼に直接払って下さい (Kare ni chokusetsu haratte kudasai, Please pay him directly). In the business world you find 接待 (settai), literally “connect-wait,” which refers to wining and dining clients as entertainment. And don’t forget 溶接 (yōsetsu, literally, “melt-connect”), meaning to weld something together.
One of my very favorite Japanese words also relates to the hand: it’s 孫の手 (mago-no-te). The literal meaning — “hand of a grandchild”—is much more elegant than “backscratcher.” Try and envisage, if you will, the contentment an elderly person must feel while being attended to by a devoted and loving grandchild, who helps relieve an out-of-reach itch.