How to calculate planet orbits?

Can anyone direct me to a website which explains how one might
calculate the orbits of the planets from observations in order
to confirm that orbits are in fact ellipses rather than some
other proposed shape? A general description would be more
useful than the detailed mathematics, but both would be good.
If no-one has a website, could you just give me an outline of
what would be involved? I'm more interested in an easy way to
do it with modern techniques than in how Kepler did it.

-- Jeff, in Minneapolis

Subtract 1 from my e-mail address above for my real address.
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