Unfortunately I have no context because it's from an exercise where the idioms are given like that, without any context, in a column, and the student should guess the meaning. (Wordbuilder by Guy Wellman, p. 29, ex. 1) Anyway, thank you!
"Finger" means to touch, with the connotation of stroking, sometimes unconsciously as in "She nervously fingered her left earring." I can't think of any other meaning with the word "document."
In slang usage, "finger" means to inform on to the authorities, but clearly that's not the usage in ex. 1. In musical jargon, "finger" means to determine the fi