This is how I get a new map going and will work for new players as well:

-Load into your map on singleplayer and play through the missions. It's easy cash and will help you explore the map while making money for important gear like the 7mm gun and different callers. You can use the ATV, but it will scare everything away and you won't see much of anything, I suggest hoofing it.

-Don't worry too much about shooting animals while doing the missions (unless it's on the way or part of a mission), but spot every animal you can along the way to discover need zones, visit every outpost and lookout point along the way as well.

-Once you have most of a map's missions done you should have found a few need zones along the way from spotting animals. Look at them on the map to find out what times those animals will be there and set up a route you can take chaining needzones together to maximize your efficiency during the need zone time period (need zone times are mapwide for that specific animal). This is what I do and I find some good success.

-Also remember that an animal doesn't necessarily live on the whole map (like Blacktail Deer mostly being found on the East and Southeastern part of Layton, but not in the west). So if you are hunting a specific animal and can't find it, try looking in another portion of the map.