How should use of a preprint server be incorporated into the publishing workflow?

Workflow may be different, but the one I am familiar with is:

• put preprint on arXiv along with sending it to a journal

• after the final version is confirmed, update the arXiv with the newest version of text (with your formatting)

• (in case there are serious mistakes or omissions, update arXiv at anytime)

Sometimes version on arXiv is put before the submission to a journal, for example:

• there is some work that need to be done before the submission, but we want to have it before a conference we are attending, or a talk at another department (so we can point the preprint to the reader),
• we haven't decided yet where or if we want to send it.

And in some cases, arXiv is used instead of a journal, especially if:

• the work is not suitable for publication in a journal (e.g. a PhD Thesis, textbook), but we want to disseminate it, preserve it and make it easily citable,
• the author prefers it that way (e.g. it is a short note, or the topic is unconventional and the author prefers to avoid struggling with editors).

The role that pre-prints have in the collective workflow of people in a field depends half on each person's preferences and half on how it gets established as a means of communications. There are no 'right' or 'wrong' workflows for using a pre-print server (though there are wrong ways to use one), and you should use the one that fits you best personally and lets you communicate best with your colleagues.

There is a broad spectrum of reasons you might want to upload a preprint, which are explained in detail in this question. To give a brief summary, you might upload a preprint or postprint

• to provide free access to your content to researchers and students in institutions without subscription to the journals you publish in, which is also a way
• to help increase the use of your papers by the community, and hence the number of citations;
• to establish priority of a result, and particularly as a way to get more widespread credit for having introduced an idea at an early stage;
• to open a manuscript up for public comment from your colleagues after you feel it's mostly ready but before you're prepared to set it in (published) stone;
• to make it visible to people who browse it often as a way to see new results;
• to cite as-yet-unpublished work in some other paper, in a way that referees of the second one can see it;
• to fulfil open-access conditions on a grant;

or for many other reasons. Whether these (or others) apply to you will determine how you use the repository. Some of these are personal choices, and may come down to how much you feel you stand to gain from non-institutional readers having access to your work. Some of these are field-dependent, and hinge on there being a significant fraction of the workers in your field that regularly check the repository.

The appropriate time to upload will typically vary on a case-by-case basis. You might upload at an almost-finished stage, at the time of submission to a journal, at time of acceptance, at the time the paper is published, or even six to twelve months after that. Each of these corresponds to some or other of the motivations above.

One thing that's important to keep in mind is that you must have a good idea of prospective journals you'd like to publish in, and of what their preprint policies are, before you upload, as it can rule out certain publication venues if you're not careful. This is again field-dependent; many physics journals take that as standard but biology ones might not.