First, like I said, the original records are housed at the Gilmanton Town Hall.  They are open to the public, but request that if you are searching "older" records, please call ahead so the staff can locate these records and bring them upstairs from the basement area.  Their hours are:
 

Mondays 9-12 p.m. and 7-8:30 p.m.
Tuesdays CLOSED
Wednesdays 9-12 p.m. and 1-4 p.m.
Thursdays 9-12 p.m.
Fridays 9-12 p.m. and 1-4 p.m.

Second, the State Vital Records Dept. at the Hazen Drive address below is the way I usually do it.  They have records for all the towns in New Hampshire and it's kind of like "one-stop-shopping".  The work area is great and is convenient to downtown Concord.  Copies can be made for the .10 xerox cost and please bring only pencils to write with--pens are a definite no.  Laptops are an OK....Their days/hours are:
 

Mondays, Tuesdays, Thursdays, and Fridays 8:30-4 p.m.
Wednesdays 8:30-3:30 p.m.
CLOSED EVERYDAY from noon to 1 p.m. for lunch.  There is a nice cafeteria open to the public there, and if you choose to leave the complex, there is "fast food" within 2 minutes on Loudon Road.  Or you can bring along a lunch!

Third, if you aren't in the New Hampshire area you can still view vital records on microfilm.  The LDS (Mormon) Church has microfilmed records for Gilmanton and these can be ordered/rented for $3.50 at your nearest Family History Center.  There are 2200 FHC in the world, so chances are you are within an hour of one.  The microfilm numbers are listed under "Microfilms" on this site's home page.

Fourth, there is the way that can get pricey, especially if you have a lot of research and not sure of the exact dates.  You can send directly to the Town of Gilmanton or to the State Vital Records and they will issue you a certified copy mailed directly to you for the cost of $12.00.  You have to provide them with the name, place & year of event (usually they will search a 2-3 year span).  Their addresses are:
 

Gilmanton Town Hall-Vital Records
Route 107
Gilmanton, NH 03837
TELE: 603.267.6726

Bureau of Vital Records and Health Statistics
6 Hazen Drive
Concord, NH 03301
TELE: 603.271.4651

Fifth, there are volunteers that sometimes do "Random Acts of Genealogical Kindness".  and also there are "GenieAngels".  These are volunteers that will look up/visit records that are close to their proximity.  I can't guarantee that they will be available for what you are looking to find, but it's well worth the time to check it out.  And, I loved the program so much, that I have volunteered to do look-ups here in my area of Connecticut.  If you have some free time, LOVE genealogy and that musty smell of old records, and wouldn't mind doing 1 look-up a month, this might be of interest to you, too.