Buy a handheld GPS.
or get a decent topographical map of your area and work it out by hand.
Or get a sextant and take a sighting of Polaris. Your latitude is equal to the elevation of Polaris. Assuming northern hemisphere, of course.
How precise?
Your profile says NYC (This is New York City, right?). Googling for ‘latitude’ found www.bcca.org/misc/qiblih/latlong.html which gave a figure of 40.4.
So (1) asking SDMB and (2) googling seem to work too. Gorsnak’s’s the most fun though.
Perhaps to OP was wondering about how to do it (measure latitude), given no access to any modern technology.
The scientist volunteers in a TV programme called Rough Science had to do just that in one episode: The Challenge: Measure Latitude and Longitude
There were two methods employed, both described in links below:
Making a Quadrant
Measuring latitude using the sun
OF course, this depends greatly on your definition of ‘precise’.
Good call on the Rough Science link, Aro – it’s an excellent program, one that most Dopers would enjoy. Unfortunately, it’s a little hard for US viewers to find; some PBS stations carry it (or did in the recent past), and the Science Channel on cable/satellite ran it a few months ago – AFAIK, they have no definite plans to run it again in the near future.
I used to frequent a weather site that told you your exact latitude and longitude. There was a clickable map that you could zoom in on so much that a city block took up half the screen. IIRC, it even had street address numbers in their correct places on the streets. You could click exactly where your house is and it would give you ultra-precise coordinates. The coordinates of my location went at least 8 or 9 decimal places out - maybe more.
I just wish I could find the damn site again. I lost the bookmark in a crash a couple of years ago and have been looking for the site ever since.
Terrafly is good for locating US Latitude & Longitude.
Or you could try Geocoding, just click on Test Drive and enter your address.
As a ham radio operator, I use that all the time.