This is difficult. It takes those who know years of practice to do it properly for their body. As the previous answer states, you need to do it carefully. The idea is to drape it around the body, but not create a skin tight suit out of a length of fabric. Look up the tutorials, and find the one that works best for you.
Since I have never draped a sari before, I cannot say what tutorials on YouTube would be best or what it would feel like to wear a sari that has been draped right. However, I can say that the end result of a sari draped right is stunning. Doing it right is the hard part; once that’s done, you’ll look amazing.
Don't attempt this alone! Have you an Indian friend who will drape it for you? If not, go to Youtube. There are a number of demos there but you want a genuine Indian sari, so try Mandira Bedi. Her demonstration is clear and she gives good tips, such as wearing one of the shoes that you intend to wear with the sari so that you get the length right. You start with the initial wrap round your body, and go on from there.
The key is to have the sari drape elegantly, not too tight so that any curvy parts of you dominate the effect, and not too long so that you trip over the hem as you walk. Using a long mirror, try out your walk in a sari before you ever go outside or wear to an event. Walking in a sari is very different from walking in jeans or even a suit skirt. Practice makes perfect, and you may well look a dream.