You will need tailoring skill and scissors to use the bag on leather & cloth
You will need Mining skill and a blacksmith tool of some sort to use the bag on metal items (And then only types craftable by a smith).
They give the following benefit:
They return ONE extra resource back for each item, based on the related skill.
Smelting Smith-type items gives you 0.66% * mining skill*ingots needed to craft, rounding the result down. At 100 Mining, one gets 66% back (or just under 2/3), so one would get 7 ingots back from a 12-ingot longsword. If one is wearing the +3 or +5 mining gloves with 100 actual skill, this puts the skill over 66.66(repeating decimal)% skill, so one would get 8 back from the 12. One starts getting 50% ingot return (without the bag) at 75.8 Mining skill
The Salvage bag adds one ingot to these numbers, so at GM (up to 101.1 skill), one would get 8 (7+1) ingots back from the longsword; 9 (8+1) ingots if 101.2 or greater with the mining gloves.
For tailoring, it SEEMS from experience that the return back from items is capped at 50% at GM, which you would then get another +1 leather or cloth back from the bag.