Do I need to cite a source when defining terms?
The purpose of defining terms is to make it clear to your readers how you are using these terms, for example because:


there is no consistent use of these terms in the existing literature,
because your paper’s audience is not familiar with these terms, e.g., due to coming from another field,
you created a concise term for some concept that you introduce in your paper.


First of all, this is not a case of common knowledge: If it were, why define at all? However, that does not mean that you must cite somebody. Instead cite somebody if:


You rely on a specific piece of work.
If you had to look up the definition instead of coming up with it yourself, this almost certainly applies.
Keep in mind that coming up with a useful definition of some things is a challenge and deserves credit.
On the other hand, as a rule of thumb, you do not need to cite if you would not know whom to possibly cite in the first place (possibly after a short literature search).
You want to affirm that you are adhering to some standard.
Using established definitions does not only make your work easier to read but also may make it comparable to other works or reüsable.
If nothing else, providing a source for your definitions may calm down Reviewer 2.


Some examples:


I would not cite in the following statement, which is essentially clarifying a well-known conflict between two common definitions (whose history I do not know):


  We here define the natural numbers ℕ to include zero.

I would cite in the following example, not only for giving credit but also for affirming my approach:


  We here define epilepsy as […].
  This is equivalent to the definition by Fisher et al (2008), except for […].
  This difference is due to the practical reason that […].






  Do I quote a dictionary, […]?


Regular dictionaries reflect the common non subject-specific usage of terms, which is by nature often broad, fuzzy, context-dependent, and different from academic definitions (if they exist).
This usage is also what you have to expect readers to understand if a term you use in a paper is not specifically defined and there is no established use in your field.
With other words, the dictionary definition is the fallback default anyway.

Therefore quoting a dictionary for definition is pointless in my opinion: it changes nothing and clarifies nothing.
If you think that a dictionary definition is the best guidance you can give to your readers, you may as well skip it.

(Note that field-specific dictionaries are a completely different thing.)


  Do I quote […] another research paper in the field, or do I paraphrase either one?


This may depend on your field, but I would refrain from paraphrasing definitions just for the sake of paraphrasing.
If I rephrase definitions, I risk changing it.
Therefore I would only do so with a good reason and when I can be confident that my changes do not affect the outcome, e.g., I could change symbols in mathematical definitions to match the conventions of my paper.

In all other cases and particularly in fields where exact words are important, I would rather use a huge quote than paraphrasing.
Still, conventions here may vastly differ between (sub)fields, so best check what is common in yours.
Either way, once you build upon somebody else’s work like this, you should cite.