First, you need to offer top quality content that is worth sharing. When people share your content they create organic backlinks and bring in more traffic which will make the video go viral.
In the video also mention that people should visit your site and give them the URL or simply tell them to find it in the description if you have your link there. Don't leave people guessing always tell them what they should do (call to action).
Send youtube viewers to a freebie/giveaway, that way it will be easier to get them to click on your link and visit your website. Also have a watermark with your website with URL and a very short description in the beginning and end or throughout the whole video.
Another thing that works is to keep adding new videos, some will bring traffic while some won't but the more you have the better. Also make sure your SEO is on point, both on-page and off-page SEO then you should be able to get some traffic to your site from youtube.
To rank your videos, make sure you create backlinks for them and have your keyword in the metadata.
Hope that helps.