Poner la mano en el fuego por alguien
 

Confiar en alguien plenamente. English?

I take you could go literal as in "to put your hand in the fire for somebody" but maybe more commonly, "to stick one's neck out for somebody", with the idea that you "take responsibility" for whatever the person may do, as you trust that person.
"Poner la mano en el fuego por algo" would be "to put your finger on something" (as in being sure of it.)
Another ways would be something like, To bet one's life on, to stake one's life on... :)

cf. Humphrey Bogart in Casablanca I don't stick my neck out for nobody, before doing exactly that.

Edit: Bad grammar - it should be anybody.

Got it! (But is this type of "bad grammar" something like Humphrey would say, and kind of be the "accepted" bad grammar an American native speaker would use?

(Like, I 'dunno' or 'ain't'... these type of things? Or is it 'worser' than that?)

Yes, it is definitely used in the lower speech registers, or for humorous effect. In serious, formal or academic speech you would not use it, nor in formal writing. In any other setting, or even in a formal setting where you want to be humorous, it could very well be used.

Gotcha! ;) :)

I mean... I grasp the significance and implications of such usages... :) :D

Good! :)

Some other possibilities for the original question:

Poner la mano en el fuego por alguien
To stick up for someone.
To have someone's back (I've got your back on this)
To back someone up.

Just right - and also "to go to bat for someone"; "to stick up for someone".