Walking on higher elevation tiles (hills, mountains) in the overland map are good for spotting large creatures.
After spotting them you have the challenge of actually taking them down. Bow and arrows are good for this. Javelins are good too if you have high spear skill. You will want good tracking skill as well in order to try and track them if they get away. If you stick with a very light load for your hunting trips (bare essentials - knife, ranged weapon, possibly a melee weapon, as light as you can on clothes which depends on season). Leave all the other stuff somewhere you can easily find again to pick it back up. At a campsite or whatever.
If your character is stealthy enough you can sneak up on them, otherwise your best bet is to just shoot or throw at them every time you see them and continue tirelessly following their tracks. The animals do eventually get tired - much quicker if you manage to wound them. Having good speed and endurance stats helps a lot with hunting. Hunting in open areas can be easier since you don't have to navigate the trees, but in those cases you won't be sneaking up on them at all - just running them down. Make sure you start the hunt well rested and alternate between running and walking to keep from getting too high a penalty due to fatigue.
If your character has low speed and endurance you may not really be suited for running down animals. In that case, your best bet is to use traps and fishing and such for food. Trap fences can be highly successful if placed in the right spot. If you find an area that you see a lot of wildlife wandering through and fence it off, you will catch animals.
You can actually run animals down with a melee weapon, it's just harder. They do eventually get so tired that you can catch them with a fast character. I actually had a character run down a stag and kill it with a knife once. He was running around naked with nothing but a knife lol. It was in an open area though so I didn't lose it in the trees.
Be prepared for it to take a while though, and don't expect to catch every one. You'll lose many in the woods, especially if they backtrack and get you confused over which tracks are which.