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TE or SHU?
手
This is the kanji which means “hand.” You will meet this kanji in many contexts—both figurative and literal. This is not a difficult kanji to memorize; even beginners can learn to write it fairly quickly. However, when you see 手in a compound word, you may be unsure of whether to pronounce it with the on-yomi (SHU) or the kun-yomi (te). The split of on-yomi vs. kun-yomi compounds is about fifty-fifty. Therefore, you have to memorize the high-frequency examples.
Here is what I mean, starting with words that begin with手. What follows are two lists: first a list of words that begin with SHU, and then a list of words that begin with te:
SHU-beginning words:
手術 （しゅじゅつ）surgery
手芸 （しゅげい） handicraft
手動 （しゅどう） manual
手話 （しゅわ） sign language
手段 （しゅだん） means, method
手腕 （しゅわん） skill; ability
te-beginning words:
手間 （てま） time; labor; effort
手不足 (てぶそく) shorthanded
手形 （てがた）promissory note
手帳 （てちょう） pocket notebook
手袋 （てぶくろ） gloves
Similarly, words that end with 手 are about evenly split between the on-yomi and the kun-yomi:
SHU-ending words:
選手 （せんしゅ） athlete
歌手 （かしゅ） singer
騎手 （きしゅ） jockey
着手 （ちゃくしゅ） beginning; commencement
te-ending words:
大手企業 （おおて）major company; big company
熊手 （くまで） rake
相手 （あいて） partner; opponent
片手 （かたて） one hand; one-handed
There are also two irregular readings of 手, ta and zu. Listed below are the only words where you are likely to encounter these irregular readings:
手綱 （たづな） reins
下手（へた） bad at
上手（じょうず） good at