How is a place's altitude determined (for example, a city's)?

Answer 1

By the use of a specialized instrument called an altimeter.

Answer 2

Mean Sea Level is determined by 26 gauging stations along the Atlantic and Pacific ocean and the Gulf of Mexico for all stages of tide over a 19 year period. The elevation of the sea can differ from station to station depending on the tide, of course. Remember that the MSL was accepted as the vertical datum in North America for a long time. However, the current vertical datum uses a single vertical benchmark in Quebec, Canada, along the St. Lawrence Seaway.
During the 1850s the United States government began a program to bring vertical benchmark data from the tidal stations across the continental United States. Around 1887 the United States Coast and Geodetic Survey started a transcontinental survey to establish vertical Benchmarks across the United States. This was somewhat completed in 1929 and you may come across some maps today referencing NGVD 1929 vertical benchmarks. Of course NGVD means National Geodetic Vertical Datum. A general least squares adjustment was performed over a large geographic area incorporating 100,000 Km of leveling runs.
Of course everything gets old due to deterioration of monuments, changes in sea level, and the shifting of the Earth's crust. So a new adjustment was completed around 1988 (actually 1991) called the NAVD88, or the North American Vertical Datum of 1988. Of course this adjustment shifted the vertical datums from the 26 tidal stations to the single vertical benchmark in Quebec, Canada. So, the elevations referenced to NGVD88 are no longer referenced to MSL. The National Geodetic Survey performed this general adjustment and included more than 1.3 million observed elevation differences.
These elevations are now placed across the continental United States and you can find one in your location by going to the NGS website and doing a search for vertical benchmarks.
Keep in mind that things are changing again as the National Geodetic Survey and surveyors use the latest GPS equipment to complete surveys and gather information about the Earth's crustal movement. New techniques about gravity and the elevation of certain points (mass of mountains) must now be incorporated into new vertical surveys.

Answer 3

First mean sea level is determined somewhere on the coast - mean sea level is the level at which the tide is below it half the time and above it half the time. From there, altitude is measured going inland by transit and stadia rod. Here in the USA, the USGS has placed markers at sites of measured altitude.

Answer 4

The barometric pressure is less the higher you go. There are instruments that measure altitude - sky divers use them to determine when to open their chutes.

Answer 5

measured from sea level - so if you live on the beach you're at 5 -10 feet in altitude... if you live in the mountains, you could be at 1,000's of feet in altitude