Enter through any entrance to Yellowstone NP and drive around Grand Loop Rd. Major junctions will be Canyon, Mt. Washburn, Mammoth Hot springs, West Thumb, Old Faithful area. As you drive around this area you can spot several species of wildlife.
Photo Spot Details
Drive through the Grand loop area you will be able to spot Deer, Elk, Bear, Bison, Wolf etc., along the road. Best time of the day is early morning as the crowd along the roads are less and you can spot more wildlife than later in the day. Always maintain a safe distance and do not approach or provoke them, park has a set of rules for each wildlife spend some time and read those instructions. As you drive if you see a crowd, park the car safely to the side and go near the crowd you might spot an wildlife. If you see too many crowd on the street with lot of photographers then that spot definitely has a bear.
Things to carry, telephoto lens, monopod or tripod. For amateurs best is to have a telephoto zoom lens like 70-300mm on a crop body or 150-600mm Tamron or Sigma S on a FX body. This way you don’t miss the nearby Bison or far away Bear. The featured image I shot was using 70-200 f2.8 lens with 2x tele-converter. I would suggest anyone to avoid this combination as it takes much practice to get the image sharp, forget tack sharp. Best tele-converter for this lens is 1.4x other than that you are hoping and praying for good light conditions. If you are hand-holding with tele-lens with VR ON, first focus (backbutton or half press) wait for VR to settle down then click the picture. I noticed this approach produced keepers with 2x tele-converter.
Most important while shooting look around your surroundings and listen to park rangers.
Some tips on what to do after spotting wildlife are:
1) Do not run
2) Do not shout, yell or talk loud
3) Don’t park your car in the middle of the street
4) Do not get closer to cubs or calf no matter what they are not your pets
5) Carry bear spray at all times
6) Do not stand alone, stay with group of people