Question

How do you figure out longitude and latitude...

Answer 1

Your question could mean one of two different things.

You could be asking "How do I figure out the longitude and latitude
of, let's say, Killeen, Texas."

The answer to that is:  You look on a map or a globe that has latitude
and longitude lines printed on it, find Killeen, Texas, and estimate its
coordinates as well as you can from the lines printed nearest to it.

Or you could be asking "If I'm out in the middle of the ocean at night,
how do I figure out the longitude and latitude of where I am ?"

I'm afraid the answer to that is far too complicated to write here. 
All I can say is: The science of "Navigation" was developed over a period
of hundreds of years.  If you look at the history of sea exploration through
the centuries, you see how the explorers ventured farther and farther from
their home ports as time went on.  The reason for that is that they were
developing better and better methods of figuring out where they were as
they sailed.

And about 20 years ago, that all changed.  Drastically.  Now, anybody at all
can walk into his neighborhood sporting-goods store, and buy a little device
that fits in his shirt pocket or in the palm of his hand, and whenever he has a
view of the sky, it can give him the latitude and longitude of the place where
he's standing, more accurately than the best navigators in the US Navy or
the British Armada could ever calculate it before.

That was when countries started putting up bunches of little satellites
to broadcast signals to our pocket receivers.

The satellites that the US put up are called the Global Positioning System . . .
the GPS.

Answer 2

Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface.

Latitude is the angular distance of a place north or south of the earth's equator, or of the equator of a celestial object, usually expressed in degrees and minutes.