So, from personal experience I'm going to make a beginner walkthrough after years of playing.

So first, you want to make sure there are no hostile creatures around. Generally where you tame them there are none, but there sure are a lot of raptors at the Lost Island place for taming them. They WILL kill the parasaur AND YOU as soon as you knock it out. Either said taming them here altogether or bring a good ptera and kill them.

So once you have made sure there are no hostile creatures, this is what you'll wanna do. Craft a bola, maybe multiple if it's a high level. Bring a club and maybe even a few tranq arrows and a bow.

Bola the parasaur, and then hit it with the club, as fast as you can before the bola comes off. Eventually this will knock it out, and you can feed it berries. You might want to bring a few narcoberries. Mejoberries are recommended for levels.

Now, you've tamed a parasaur! Once it's tamed, you still have to make sure it doesn't die. You should probably bring another tame in order to keep it safe, or just pump all it's levels into speed and stamina.

Thanks for reading, hope this helps!

-SangToareGirl (Author of Valguero's Guardian and The Five Talons of Abberation)