Obituaries and death notices are two of the primary ways to announce someone's death. They appear in local newspapers in the place of residence and/or death of the person, and make an essential resource for genealogical or biographical research. While death notices tend to be shorter and do not contain much information beyond the name of the person, the date of death and the time of the funeral service, obituaries often read like biographies in their own right, listing the achievements of the decedent, the highlights of their life, likes and dislikes, and also family members who had predeceased them and those who have survived them.
A third document that could be used in the absence of an obituary or a death notice -- a situation that should not be discarded as possibility unless you are completely certain there is an obituary -- is death certificates. The New Hampshire Division of Vital Records Administration over at NH.gov is the custodian of vital records in the state but you should know that, unless you are an immediate family member or a legal representative, you can't access records less than 50 years old. However, death records older than 50 are considered public and anyone can access them after submitting a written request. One great advantage of the NHDVRA is that it also keeps a genealogical database of vital records going back as far as 1640. Help from volunteer genealogists is also available.
As for obituaries, you have several options, depending on how much information you start out with. If you know the full name of the decedent, the date of death, and the name of the newspaper that carried the obituary, you can simply contact it and request a copy of the issue. However, this is an ideal situation: in reality there are a few stumbling blocks that can make you choose another option. For one thing, not all New Hampshire newspapers keep an archive of their complete run. For another, you may not know the name of the newspaper, and may not even be certain that there is an obituary. A third problem would be if there is an obituary but the newspaper in which it appeared is no longer in circulation.
There are a number of websites where you can search for an obituary using only the last name of a person. This can be the best option if you don't yet know much about that person.
Most of these websites are free to use, while a minority require free or paid subscription. The minimum information a search of these databases would yield is the full name of the decedent, the date of death, and the date of publication of the obituary plus the name of the newspaper. Some will give you the full text of the announcement, and some would even display an image of the actual obituary as it appeared in the newspaper.
While most of these websites have quite extensive resources, they are not comprehensive, so do not be surprised if your search fails to yield any results. It may be that the newspaper that carried the obituary you need is no longer in circulation, or it may be that there was no newspaper obituary, among other reasons. If this is the case, then it is time to move to another source.
If you don't have much information about the object of your research, you can enlist the help of your local library or, if you know the place of residence of your ancestor, the library there. Local libraries are very often an invaluable source of genealogical information as they may keep more local history resources than bigger, more central ones. Of course, every library keeps newspaper records and these invariably include titles that have gone out of circulation. What's even better, some libraries have indexed specifically obituaries, which could save you a lot of time.
The Conway Public Library, for instance, has a database of obituaries from the North Conway Reporter, a local title, from 1895 to 1991, as well as an index from the Conway Daily Sun from 1989 to date. What's more, the library also keeps birth and death records entered in the Annual Reports for the Town of Conway, starting from 1880. The indexes are searchable online by name, date and place of birth and death, and by names of parents.
The New Hampshire State Library (accessed from NH.gov), for its part, has a collection of over a hundred local newspapers on microfilm, some dating back to the early 19th century. This makes for a vast database of information, including obituaries. On the website of the library you can see the full list of titles that are part of the New Hampshire Newspaper Project, as well as the range of issues they library has. These are available to buy.
In New Hampshire there are also a range of local resources, some of them extensive. For instance, a website dedicated to cemeteries in Bedford offers a list of decedents in any given cemetery in Bedford, with a lot of information including their date and place of birth, along with the date and place of death, name of spouse, and, if there is one, obituary. In Hillsborough county there is also a countywide search tool online, which you can use by entering the last name of the decedent only. The information you will get includes the full name of the person, dates of birth and death, and the name of the cemetery where they were buried. For some, there is additional information such as immediate family members, or whether the person died in a war, and which war it was.
These associations can be just as valuable sources of information as libraries. Some have local newspaper collections, and due to their specialized nature, they may very well keep records unavailable elsewhere. These may include cemetery records, inscriptions, vital records, and church records, along with family histories. Some of these are available online but even if they are not, contacting the society and making the trip to its headquarters may be worth the effort, if you cannot find the information you need anywhere else.