I haven't done much fishing when out doing bushcraft things (mostly because I've never been close enough to any lakes/rivers that would merit fishing!). However, I carry a box of hooks, a reel of line, and some weights in my pack, as well as a small plastic fishing float that I found many years ago. This all fits in a small tin, so isn't a noticeable amout of extra kit to carry.
However, the bear minimum you need is some kind of line, a hook, something to weight it down with, and some bait.
Line can be any kind of material - cotton thread/string/paracord, or woven plant fibres are good (however fish are less likely to bite on a visible line).
Hooks can be made out of a lot of different materials as well, from bits of bent wire (paperclips etc) to plant thorns, wood, bone etc.
Bait can be insects, bread, or for predatory fish, something that looks like a smaller fish (foil, shiny plastic etc).
Floats are useful if you plan to leave a line sitting, but don't want to be holding on to it to notice bites/nibbles - floats can be very easily fashioned out of elder stems, as these have a pithy core and float well.
Bear in mind with all fishing that some days, fishermen with the latest and greatest lines, lures, baits, rods etc will fail to get a single bite - so don't be disappointed if you don't get anything with a more home-made set of kit :?:
And one last important note - always make sure that you don't discard used line/hooks etc, as these have a seriously detrimental impact on wildlife, particularly birds which often get tangled in used line. If you have some spare and nowhere to dispose of it, burning is the best way to get rid of it.
