It's best to install extensions (as well as to patch and upgrade your site) on a development server. In other words, you install and change a development copy of your website. You then test to see if everything is working as intended, and make sure that the changes didn't break anything vital to your site. Adjustments may in some cases be needed.
Then, you push the changes out to your live website. You (often via your web hosting provider) should always have recent backups to fall back to should anything go wrong in the process. This is just an overview for illustrative purposes.
Maintaining and improving a Magento website is best done by an experienced professional that has various prerequisite technical knowledge. You can learn more about installing Magento 2 extensions at: https://docs.magento.com/marketplace/user_guide/buyers/install-extension.html , but my advice would be to hire an experienced Magento developer.
I'd tell you the same about various other professional services, like plumbing or electrical work. You may be able to do it on your own, but if you're relying on your website as part of your business, and you're not a web developer, it may not be a good allocation of resources, and you may risk doing harm to your online store and sales.
If you'd like some recommended Magento dev teams or freelance developers to consider, I know many, and would be happy to try to make some recommendations.
