You can go to the Vermont State Archives website. They have a form for you to download to request vital records (non-certified copies), which are free. You fill out the form and email it to them and they respond with the record or they will tell you if they cannot locate it. If you want certified copies the fee(s) is listed on their site.
Here is their website which has all the information you need:http://vermont-archives.org/certifications/
You can also search on the LDS website (www.familysearch.org
) for Vermont Vital records and the same records are located there--most of them.
Searching on the LDS site, I found a Norman Smith, b. about 1855 at Winslow, Quebec, died 3 Nov. 1901, at Derby, VT, parents are Angus & Ella Smith. No place of burial is listed:https://familysearch.org/pal:/MM9.3.1/TH-266-12121-117707-5?...
This record for Norman's death on the LDS site is probably quite similar to what you will get from the Vermont State Archives.
When you have an exact date of death mo/day/yr, you can request an obituary search from the Vermont Dept. of Libraries. They have most Vermont newspapers on film there. They will email the obituary directly to you for free. Here is their website:http://libraries.vermont.gov/contacts
Sometimes obituaries will tell you where a person was buried.
If you cannot locate the record/records from the Vermont State Archives or the LDS site, you may have to write to the town/city clerk where the event occurred and request information directly from them (have them search their records). How to contact town/city clerks for each Vermont location you should be able to find online.
Hope this is helpful.