For me, the answer to the question "Is there one generic process a researcher can follow to figure out what records are available for a particular place and time?" starts with a review of history, including learning what laws existed in that time and place which required people to keep records.
My checklist looks like this:
- Learn what records might have been created in a particular time and place.
- Research which of those records might still exist, and which records are accessible to the public (not subject to privacy restrictions).
- Research what repositories might hold those records.
- Research which online repositories might hold those records.
The original question started from #4 and asked #3, thus the previous answers have addressed that issue. But if you don't establish a timeline first for what records were taken, you can spend a lot of time looking for things that never existed, or didn't survive. So for any given place, before you look for census records, it helps to know the answer to the general question of when the census was taken. There's no point in looking for a nationwide 1831 Census of England and Wales, or a 1780 US Federal Census.
Researching the first question in an area's archives will usually reveal the answers to the second question (e.g. that the Population Schedules from the 1890 US Federal Census were destroyed by fire and very few schedules remain). But if you don't ask, you can spend a lot of time wondering why you can't find the records you are looking for, when the answer is "they never existed" or "they existed but they don't survive".
The process of answering questions one and two will also differ for each time and place, just as they do for question three, and there is no simple answer unless you say "ask an expert". National Archives, and State and Local Archives, can be a great place to start; check ArchiveGrid for holdings.
For finding aids and reference guides, the US National Archives (NARA) has Prologue Magazine, with in-depth articles; their articles posted online about US Naturalization records are superb. For general knowledge about the UK, there is Herber's book Ancestral Trails; there are also many research guides at The National Archives (TNA).
Researching what newspapers were published can also turn up the answer of where you might find the newspapers offline -- for the USA, try the US Newspaper Directory, 1690 - Present at the Library of Congress' website, part of their historic American newspapers project Chronicling America.
But to me, if you have reached the point where you have exhausted the available online resources, and you haven't already established the larger context, it helps to stop a moment and review the history of the area you are researching. For the US, it helps to know when the town was established, when the county was created, what the previous towns and counties were, the year of statehood, and so on. Explore the terrain if you haven't done so already -- for marriage records especially, couples might have married in the next county over, if the county seat was easier to travel to.
Perhaps you have already thought about all those things; if so, I apologize for pointing out the obvious. But I think it needs to be repeated, because online services can give the impression that they cover more ground than they actually do, and sometimes the reason why you can't find things is that the newspaper wasn't published that year, or the records existed but don't survive. Starting with the question "what might exist" gives you a fresh perspective.
One strategy I use to find records I didn't know about is to read case histories from other genealogists. I see what records they use in their searches, then I ask if equivalent records might exist for the time and place I am working in. Search WorldCat, JSTOR, and other library catalogs for genealogical periodicals and books, to find prior research in a geographical area. Read the bibliographies and source lists for clues to what might be available. My other finding strategy is simple: whenever I ask "do you have X" and someone says "No, we don't have that." I follow up by asking "If you were looking for X, where would you look? Who else might know?"
My generic process for finding records for a particular time and place is not unlike what I would do when finding information about a person. Start with what you know, and work outwards from there. Break the big question down into smaller pieces, and try to answer the smaller ones. And if I can't find something, my #1 strategy is to look for something else, because I often find things when I wasn't looking for them directly.
Resources for looking up the original statutes:
To see an example of how a skilled researcher applies knowledge of the law to the analysis of a particular record group, see the post “Liable for training” from Judy G. Russell on her blog The Legal Genealogist. She answers a "how old did he have to be" question from a reader about the United States' WWII Draft Registration Cards, including a timeline of the seven different registrations, and links to the statutes consulted for the answer.
Whatever locality or subject you're looking for, it helps tremendously to look for finding aids or research guides written by others who are already familiar with the place and topic.