For sentence fragments, you can usually omit the subject (when it's clear what you are talking about) and any auxiliary verbs.
E. g., "Done!" means "[It has been] done."
Or, if the general context is discussing a software bug, "Fixed" means "[It has been] fixed."
"Care to comment?" means "[Would you] care to comment?"
"Finding this difficult?" (in a conversation) — "[Are you] finding this difficult?" If there is just two of you talking, it's clear that what is meant is "Are you...."
If you watch some American TV shows, you will regularly hear such subject-less and verb-shortened phrases like "Get any sleep tonight?" ("[Did you] get any sleep tonight?"). Or, "Storm's coming. You see the weather?" ([The] storm is coming. [Did] you see the weather?" (this one is from Blacklist S05E09) From the same episode, "You get that VHF radio working?" ([Did] you get that VHF radio working?)
This wouldn't be discussed in grammar books because these phrases are, strictly speaking, agrammatical. A student of a language needs to first understand the correct structure of sentences; once s/he is familiar with them, s/he can also know where it's permissible to deviate from them in colloquial settings.
There are whole phrases which are incorrect on purpose; they are used playfully. E. g., "Long time no see" (We have not seen each other for a long time).
Of course, in dissertations, complete and grammatically correct sentences should be used. On Twitter, anything goes; the shorter the better.
Here is another question where examples are given.