Old English findan "come upon, meet with; discover; obtain by search or study" (class III strong verb; past tense fand, past participle funden), from Proto-Germanic *findan "to come upon, discover" (source also of Old Saxon findan, Old Frisian finda, Old Norse finna, Middle Dutch vinden, Old High German findan, German finden, Gothic finþan), originally "to come upon."
The Germanic word is from PIE root *pent- "to tread, go" (source also of Old High German fendeo "pedestrian;" Sanskrit panthah "path, way;" Avestan panta "way;" Greek pontos "open sea," patein "to tread, walk;" Latin pons (genitive pontis) "bridge;" Old Church Slavonic pǫti "path," pęta "heel;" Russian put' "path, way;" Armenian hun "ford," Old Prussian pintis "road"). The prehistoric sense development in Germanic would be from "to go" to "to find (out)," but Boutkan has serious doubts about this.
Germanic *-th- in English tends to become -d- after -n-. The change in the Germanic initial consonant is from Grimm's Law. To find out "to discover by scrutiny" is from 1550s (Middle English had a verb, outfinden, "to find out," c. 1300).
"person or thing discovered, discovery of something valuable," 1825, from find (v.).