Always stay crouched while taming. And never get close enough to touch it. While following the monkey, if the monkey ever stops, its very likely It will turn and start to walk in a different direction. So be aware that it might walk in your direction. Hope this helps : )
You can place helmets on it too. I place my mining helmet on my monkey and use it as a source of light at my base. But you cannot see the light if the monkey is on your shoulder and your looking in first person. You can see the light in the orbital camera, While riding on another Dino in 3rd person, and when the monkey is on another persons sholder or on the ground. Hopes this comes in handy : )
Okay so, basically the easiest way to tame these cute little guys are to keep your distance and make sure they don't face you. Put Mejoberries into the last slot of the hot bar and quickly run up every now and then, feed it, and then run back to a safe distance. It can be tricky but patience is key. Also, if you are a high enough level, dodo kibble can be used instead, if you wear a ghillie suit it has a lower chance of noticing you.