Find, found, and fund could conceivably be related on the basis of the notion of obtaining something, but the words (except in the case of the link between find and one of three broad senses of found) stem from independent sources. This post defines these words and others derived from them.
Find, in the sense of discovery, is from the Old English verb findan, meaning “come upon,” “discover,” or “obtain.” The past tense is found, but the homograph found, from the Latin verb fundere, meaning “cast,” “melt,” or “pour out,” is unrelated, as is founder (“collapse,” “disable,” “fail,” or “sink”), stemming ultimately from fundus, a Latin noun meaning “bottom,” by way of the verb form fundare.
A find is something discovered or located, including a person, place, or thing with exceptional qualities. Someone who finds is a finder, as in the phrase “finder’s fee,” which describes a commission received for helping someone identify a financial opportunity. A finder is also an auxiliary telescope, and a viewfinder is a device on a camera that aids the user in focusing on the photographic subject. A finding is the result of an examination or investigation, while found serves as an adjective as well as a verb, as in the phrase “found object.” From the past tense of found, foundling describes an abandoned infant who is discovered, and something newfound has just recently been located or discovered.
As mentioned, found in the sense of “establish” has a distinct etymology, as do its kin: founder (“one who establishes”); founding (a verb and adjective referring to establishment, as in the phrase “Founding Fathers” to refer to the men instrumental in establishing the United States); and foundation, which pertains to establishment, to an organization that supports an endeavor, to the substructure of a building, or to a cosmetic base or a supporting undergarment. Foundational and foundationally are the adjectival and adverbial forms.
Something that is well founded exists with literal or figurative support, such as an organization or a theory, respectively. Something unfounded, by contrast, has no basis of support, as in the case of a rumor; foundationless is also employed for this sense. (These terms apply only to the figurative sense, however.)
Fundus, mentioned above as the forebear of founder, is also the basis of fundament, meaning “base,” and its adjectival form, fundamental. That word is also a noun pertaining to basic principles, thus the use of fundamentalist and fundamentalism to refer to Christians who interpret the Bible literally. Profound, meanwhile, retains only the figurative sense of its ancestor, profundus, and means “intellectually deep,” and fundus was borrowed directly into English in the anatomical sense of the part of a hollow organ opposite its opening, such as the back of the eye.
From fundus we also derive fund, meaning “capital” or “stock” in the sense of a financial base (as a verb, it means “supply with money”); funds and funding refer to money, the former in a basic sense and the latter in the sense of providing funds. Someone who funds is a funder, the withdrawal of funds is defunding, and the return of funds is a refund, while replenishment of funds is re-funding; something without financial support is unfunded.
A fund-raiser (the word is sometimes styled fundraiser), meanwhile, refers to an event intended to raise money from admission fees and donations, and crowdfunding (also called microfunding) is a funding strategy involving encouraging widespread but modest financial support for a project from the general public rather than focusing on a small number of large-scale investors.
The verb found in the sense of “cast metal” and the noun form founder are rare, but foundry, referring to the art of casting metal or to a location where the art occurs, is somewhat more familiar.