I wish I could find a more directly way to phrase this question, but as an English speaker learning Russian, I rarely use the word 'ведь'. I am interested in two things from native speakers: 1) In your view, is 'ведь' necessary to use in order to express some thoughts/types of sentences (examples are very welcome), 2) If so, how do I incorporate it more into my speech? How would you recommend conceptualizing it?
Typically, ведь is a part of a phrase explaining the reason for something, most often it's a reminder that the reason is known (or easily understandable) to those addressed. It sounds like 'as you know', 'as we both know', 'as everybody knows','as I already knew' , 'since', etc.
Мыть посуду придётся тебе, ведь это ты оставил тарелки после еды.
(It's your turn to wash the dishes since it was you who left those plates on the table after dinner.)
Я поспешил скрыться, ведь он собирался меня убить.
(I made a quick escape: I knew he was going to kill me.)
P.S. Where to use or not to use it. As with the equivalent expressions above: in official documents, something like потому что (because) should be used instead. In case of a dialogue or some interactive writing ведь implies the listener or reader would definitely agree with what is said or written just after that word.
By using ведь in a question, you make it sound confirming something you already know (ведь is etymologically related to "I know"):
Это ты разбил чашку? // Was it you who broke the cup? (I'm genuinely interested)
Ведь это ты разбил чашку? // It was you who broke the cup, wasn't it? (I'd be surprised if it wasn't you)