寻, 寻找 and 找
xún, xúnzhǎo and zhǎo

These three are all verbs meaning “to try to find or get certain people or things”. The objects of the three words can all be concrete things or people who are lost. The objects of 寻找 and 找 can be concrete things as well as abstract things. 寻 and 寻找 are usually used in literary language, while 找 is rather casual.
(1) 为了找到丢失的钱包，他几乎把车站都寻（寻找/找）遍了。
(2) 在黑暗的统治下，那个年代的有志青年都在努力为国家的未来寻（寻找/找）一条出路。
(3) 他找了一个很漂亮的女朋友。
(4)我们都在苦苦寻找那些丢失的纯真。
(5) 我想找一块合适的布料来做一件衣服。
(6）公告栏里贴了一则寻物启示。

In example (1) and (2), the three words are interchangeable, only that 找 is the most casual (3) and (5) are general speaking, so 找 is used. The object in example (4) is an abstract thing and so 寻找 is used. 寻物启事 in example (6) is an idiomatic phrase where 找 and 寻找 is not used.

找 can be reduplicated.
(7)我这里没有你要的书，你可以去别的地方找找。

Besides, 找 also means “to return the extra money”.
(8) 我给了他10元，他找给我2元。
(9) 我忘记找钱给他了。

三个词都是动词，都有为要见到或得到一定的人或事物去尽力的意思。三个词的宾语都可以是具体的丢失的人或物等。“寻找”、“找”常用于书面语，“找”的口语色彩较浓。
在(1)(2)中，三个词可以换用，其中“找”更口语化。(3)(5)都是日常用语，一般用“找”。(4)中，宾语比较抽象，所以用“寻找”。“寻物启事”例(6)是固定搭配。
“找”可以重叠。
另外，“找”还有把多余的钱退还的意思。