If it is a hex crawl and survival-themed game where hunting can easily become part of the encounters, I use a mix of encounter tables, skill checks, and perhaps combat. The encounter table will tell me what is in the hex. But instead of rolling for a random encounter, I'm using it to tell me what creatures are likely to be encountered. In a survival based game, I may have a separate flora and fauna list to go with different environs/hexes so I don't muddy up random-encounter tables.
The player needs to tell me what they are hunting for and how they are doing it. They may need to make a survival check to find a tracks to track or a path to set a trap or tree-stand at. They may need to make a stealth roll to avoid spooking the animal. For large game that are found, there would be a combat to see if they can hit it before it gets away.
My rules are not codified. I call for checks based on character's declared actions and apply RAW the best I can based on my own moderate experience hunting and fishing.
Now, if this is an activity that party wants to do while travelling and the travel is not integral to the plot. I typically ask each player to tell me how they are contributing to the success of the travel. One party member may be scouting ahead looking for danger, another may be hunting and foraging for food, and so forth. Each player makes three rolls for their character using skills applicable to how they are contributing to the travel's success. 3 successes = better than average success (a bounty of game, no rations need to be used, maybe kills that bring in high value furs, etc.). 2 success = expected results (for hunting/gathering enough food is found that the party only uses half the rations they brought). 1 success = negative result (no game found, party must rely entirely on rations, or perhaps the hunter was ambushed by peryton when he was field dressing a kill, which you can play out as a combat, or just narrate average damage of one attack).
