The chains go around the bucket and under the steal beam.
Yes.
Do the chains go into the ground and hook on to something?
No.
The whole Idea is when you crank up the jack to straighten" go beyond"
Yes.
but that wants to lift the bucket.
No, it won't lift the bucket, only push the middle of the lower edge up in relation to the ends of the bucket.
f you put something heavy in the bucket on each end, wouldn't that work?
No need to put anything in the bucket.
The ends of the bucket are very stiff because of the end plates, The center of the bucket is not anywhere near as stiff. (that's why it bent in the first place)
When the jack is extended, the chains come taught, (you should make a real effort to keep them the same length) and the middle (the "smile")
has to bend upwards. Bend it slightly beyond straight to allow for spring back, release tension and check your progress. You might need a couple tries to get it right, and maybe you might ave to move the jack around, depending on how "even" the smile is.
And it doesn't have to be perfect, it's a tractor bucket.
We ain't building a church here.