"Conjunction" is a fairly broad term that can be used for a variety of elements linking clauses. If you can identify clauses and there is an element between them, you can call it a conjunction. More specifically you can try to determine whether the relationship is
coordinate or [/i]subordinate[/i], and then refer to it as a "coordinating conjunction" or "subordinating conjunction".
The Coordinate Structure Constraint (Ross 1967) is one test that can be used for coordination: that you cannot extract non-parallel elements from half of what is coordinated:
*What did you drink soda and eat?
However, that doesn't doesn't always work:
Who did you go to class and meet?
And coordinating conjunctions can also coordinate sub-clausal constituents ("mother and father" or "sing and dance"), and there is some debate about whether that is directly related to the same structure as clause coordination.
As for clausal subordination, that's also a complex topic, with various different types of subordination, and also some other approaches to labeling the "conjunctions" (which is a pre-theoretical term), for example calling those that mark
complement clauses "complementizers" as in "that": "He said
that he was..."
And there are also other more complicated distinctions, such as various hybrid ideas like cosubordination, pseudocoordination, pseudosubordination, para-hypotaxis, etc. (For more details, see:
http://linguistforum.com/typology-and-descriptive-linguistics/incoordination-(sentence-initial-counterparts-of-'and')/msg32780/#msg32780)
The point is that this topic is either relatively simple (from a traditional or causal descriptive perspective) or very complicated (trying to get the right precise description or theoretical analysis today).
I'm not sure about "tests" to check for conjunctions
per se, but I can imagine some ways to investigate the topic, depending on the circumstances.
Could you give an example of the sort of situation you're thinking about?
I'll just conclude for now by saying that although there has been a lot of research (I'm working on related topics myself), there is no consensus yet on exactly how to deal with clause combining, so some of the "answers" will also depend on your perspective/theory.
I can probably recommend something more specific if you can explain your topic a bit more.
--
Ross, John Robert. 1967. Constraints on Variables in Syntax. MIT Ph.D. dissertation.