Strike a balance: Enough information that you can actually find materials, but not so much information that it's clear you're examining already thoroughly-trodden ground.
A basic rule of thumb: If there's a lengthy Wikipedia entry on exactly your topic, that's thoroughly-trodden ground. Use the Wikipedia entry as a springboard to the more obscure.
Another rule of thumb: if it's hard (but not impossible) to find information, you're probably on the right track.
Starting points: You might be interested in a time period, or an event. You might be focused on a place: a town, a county, a state. You might be interested in a concept or issue. Whatever your starting point is, you will ultimately be pursuing individual people, particular groups, and events. The trick is in getting from the broad scale down to an appropriately narrow scale that you can find materials. Most of the tools presented here should help you achieve that task.
This is hard work: From time to time, it will be monumentally frustrating. Keep at it. Sometimes it takes dozens of false starts before you get the right combination of scope, search terms and resources. Ask for help. My contact info is on this page, and you know how to contact your professor. Look at the acknowledgements page of any academic book; professional researchers get help from dozens and dozens of people. It's not cheating; it's actually how any of this gets done.
If you start with a date range, your most helpful resource is some kind of timeline (sometimes called a chronology). There are many print chronologies; though they are harder to find and search, they often will surprise and delight in ways that online interactive chronologies won't, and are often more focused on a particular theme or location, and hence more detailed.
Starting with a year or era means you will have to find particular places, events, or people you'd like to narrow your search down to, because these are all more readily searchable than date ranges. So, a date range is a good first step, but only a first step.
A name is a good beginning. If the person turns out to be prominent (and plenty is already written about him/her), a short biography may turn up other names or events worth pursuing. A quick search in a newspaper archive may also reveal personal, business, or political relationships worth exploring.
If you start with a concept or issue (e.g. abortion in 19th C. Boston), your best bet is to find an overview of the topic that includes a section on its history, such as you might find in the Oxford Encyclopedia of the Modern World, which provides a historical overview of abortion, a section about the 19th Century generally, and a bibliography that includes entire books that cover the period with links to our catalog.
Another option, of course, is to search the library catalog. Remember: the more terms you include, the fewer results you'll get in your search. If you search: abortion, 19th Century, boston, you will get 0 results. If you search abortion (as a subject term) and 19th, you get a few useful results. If you search: abortion OR contraception OR birth control as subject terms, plus 19th, you get even more results.
Finally, you could search a scholarly article history database such as America: History & Life. I don't recommend starting here, though: scholarly articles can be so focused on a particular detail or concept that you don't get the context offered in books or overviews.
The key, though, is that you're trying to hone in on details. Overviews, books, and articles might lead you to a few details which you'll then want to pursue in primary sources. (Look at where, who, and when.)
Starting with a place will help you arrive at people or events in that place. Most towns have readily accessible historical societies; even if the bulk of their collection is not online, websites will note prominent people and significant events, and likely include photos or accounts.
Historical maps will help unearth major property owners (often noted in land boundaries), historic place names that are no longer used, buildings that no longer exist, companies, etc.
If you choose to do research on an event, person, or place in Massachusetts, of course, you will have much more material ready to hand because of the wealth of local resources: historic homes, where you can get a feel for the life of a particular era, museums and archives, where you can see objects that people may have used or read, and the neighborhoods, towns, and landscapes where you can explore where events took place. When you write, in addition to facts, you need inspiration. The web is a remarkable font of information, but less often a font of inspiration.
While searching electronic resources, try at least to find digitized images of original texts, rather than electronic representations.
Which option below, A or B, connects you to the past more directly?
A. 
B. John Hancock [signature]
