Is there any pattern or logic in word formation? For instance: Suppose we have the verb "associate" its meaning is: "to relate two things, people, etc" now the noun of that verb is "association" but it has two meanings: "an organization of people with the same interests or with a particular purpose" and "a connection or relationship between two things or people". Now why does the first meaning have nothing to do with the verb? Is there any pattern or logic? It's very weird and illogical
"Association" is actually one of the more logical words in English. Here is its etymology:
mid-15c., "join in company, combine intimately" (transitive), from Latin associatus past participle of associare "join with," from assimilated form of ad "to" (see ad-) + sociare "unite with," from socius "companion, ally,"
Intransitive sense of "have intercourse, be associated" is from 1640s. Earlier form of the verb was associen (late 14c.), from Old French associier "associate (with)."
If we consider the fundamental meaning "join in company with, or befriend" then it's perfectly logical to say an "association" is a group of people who associate with each other, and from there to "an organized body of persons with a common purpose".
Other meanings of the word play off of this meaning, as in two related thoughts or ideas that are "friendly" or "joined in common purpose". For example:
Americans often associate drinking coffee with eating breakfast, or some kind of morning activity, but many cultures prefer to drink coffee after dinner.
Here I say actions of "drinking coffee" and "eating breakfast" are closely related, as if they are a kind of combined idea.
Many other nouns that end in "-ation" or "-tion" follow a similar pattern. For example, as Tᴚoɯɐuo says, relate becomes relation. Others
combine ⇒ combination
register ⇒ registration
frustrate ⇒ frustration
cultivate ⇒ cultivation
populate ⇒ population
celebrate ⇒ celebration
and many others.
The answer to your question is, "yes, but not enough to be very useful to learners".
There are usually several different patterns, and lots of exceptional cases.
Some of the patterns make sense only if you know something about the origins of words (for example, the privative prefixes in- im- il- and ir- is normally applied only to words of Latin origin, a- and an- nearly always to words of Greek origin, and un- usually to words of Germanic origin). But if you are not aware of the history of the words, that is no help.
Similarly, derivation is often logical, but not reliably.
As Andrew points out, "association" is pretty logically related to "associate".
There are lots of rational and consistent rules for forming new words out of other words. Like the one you allude to here: "Put -tion on the end of a verb to turn it into a noun." There's, "Put "un-" in front of an adjective to indicate the opposite meaning, like "intelligent" and "unintelligent". "Put -er or -or at the end of a verb to indicate someone who performs the action", like "think" and "thinker". Etc.
The problem is that there are lots of such rules, and they aren't applicable universally. Like people who "associate" may be an "association", but people who "think" aren't "thinktions", nor do we call the act of thinking "thinktion". Something that isn't "available" is "unavailable", but something that isn't "tall" isn't "untall". Etc.
You can try to invent a new word by applying one of these rules when that isn't already an accepted word. Sometimes people will accept it and sometimes not. Like "uncool" is becoming an accepted word. I don't suppose "thinktion" is going to catch on.
So knowing the rules can help you to guess the meaning of an unfamiliar word when you see it. But it doesn't really help you to guess words with a desired meaning. That is, if, to take a simple example, you know that "white" is a color, then if you see the word "whiten" you could guess that this is a verb meaning "to make something white". But knowing that "white" is a color doesn't really help you to guess at a word for making something white. You could guess "whiten", but you could equally reasonably guess "whitize", "whitify", "enwhite", or many other non-words.