A Bug is an erroneous operation on the website based on the user experience. Resolving that issue is called Bug Fixing.
What are the common Bugs/Errors
There can be many more types of Bugs/Errors in a website development like: Text Errors(spelling & grammer Bugs), Code base Bugs, UX(user experience) based Bugs, contact fomr is not submiting, Responsive view Bugs.
How do I find Bugs on my website
Technically this is the job of application tester, this is the person who is professional for this job. But if the website or applicaion size is not too much, then a webstie developer can also do this.
How do we fix bugs of a website
This the job of a professional website developer.