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I came by some graphs showing the declination for sun and moon (between angles of -30° and +30°). The graphs look very much like sine waves.

I googled a bit and read about what the declination is, and I found tools to look up the declination for a certain date. However, what I really haven't understood yet is, how to measure the declination. So if I would like to create such a graph during the next 365 days by hand, what exactly would I measure?

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You'd wait till the sun was at the highest point in the sky for the day, and measure the angle it makes with the vertical.

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  • $\begingroup$ If you measure both parameters you can make a solar Analemma like the ancients: en.wikipedia.org/wiki/Analemma $\endgroup$
    – user6972
    Sep 7, 2013 at 18:30
  • $\begingroup$ are there any tools to precisely measure the angle (is a sextant the right tool for that?) $\endgroup$
    – navige
    Sep 8, 2013 at 10:50
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    $\begingroup$ @navige: a sextant would definitely work. Make sure to have a filter on it so the sun doesn't blind you. $\endgroup$
    – Jerry Schirmer
    Sep 8, 2013 at 18:32
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Plant a stick in the ground vertically (use a level). Length of shadow / length of pole = tan (declination).

Declination is the angle the sun makes with the zenith (direction pointing upwards--the stick's axis)

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