How about a website that has 4 pages with list and detail view structure?
Hope most of the users will be aware of using browser back button to go back to previous screen. Or should we provide a custom back button on the website?
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You should not do this.
Users know about the back button. "The Back button is the lifeline of the Web user and the second-most used navigation feature (after following hypertext links)". Jakob Nielsen in 1999. Or a Firefox study in 2010: "Across Windows, Mac and Linux 93.1 percent of users clicked the button at least once over the course of a five-day period."
So if the functionality is already there, and users already know how to find it, why include a redundant version of it in your site?
At best, users would understand that your back button has exactly the same functionality as the built-in one in the browser. That would make it simply redundant, a waste of screen real estate and one more tiny bit of unnecessary extra cognitive load for the user.
At worst (and more likely than the best case), the user is going to assume that you wouldn't put purely redundant functionality in your site -- because why would you do that? -- so will experience confusion while trying to figure out in what way your back button differs from the real one.
If your intention is to duplicate the exact same feature as the browser back button, then I would say a customize back button is a bit redundant. I can think of situation whereby a customize back button would be problematic. Say you access a subpage via url or bookmark, then the back button makes no sense at all. You also risk confusing the users on their whereabouts when they clicked on the back button. In such situation, a breadcrumb would be more ideal.
People sometimes get confused between whether it actually goes back in browser, or goes back to a preset page, for example if it just links to another page that the website thinks you've visited.
This depends on the type of UI. When you implement the browser back function, then don't. But when you for example show an overlay (i.e. some preferences dialog) over the current page, it is possibly wrong to rely on the browser back button (which could be achieved via history API) to go back to the previous activity. Then a arrow-left button would be more clear as the action is more perceived as moving the dialog out of view than as going back.
I mostly agree with adamsoh. Some audiences may need more 'spoon feeding' than others to navigate around though. In which case I would consider offering some extra on-screen navigation. If you’re worried the site may need that ‘back button’ there’s a good chance your gut feeling is correct.