How to have multiple icons for multiple instances of the same program?

There are easier ways to switch windows/apps than using the Dock. Most native, is by using the Mission Control. You can activate Mission Control several ways, on laptops it's usually F3 (without the Fn key), from Trackpad/Keyboard (check preferences) then select which app and window you want. You can also group windows by app: Mission Control > check "Group windows by application." Use two-finger scroll to zoom-in on specific app when grouped.

Couple useful shortcuts:

• ⌘+Tab: Switch between apps, use w/ Shift(⇧) to go in other directions.
• ⌘+`: Switch between windows of current app, use w/ Shift(⇧) to go in other directions.

Check out Keyboard Preference Pane for other shortcuts, or customise any.

You should use spaces, if you already aren't, this will help you sort out apps and create a better workflow.

EDIT: I forgot to answer your big question. To have multiple icons for each window, though it's not recommended; it'll mess up the mission controls and confuse you, you'd have to do it through Terminal: open -n -a Google\ Chrome; -n for new instance, -a specifies the name of app. You can also supply files after that so it'll open those files with the default or app supplied. Do man open to read more about it.

Apple has very intentionally designed against the idiom of having a task bar.

I would try enabling three finger swipe down (a.k.a. App Exposé) which lets the standard have Mission Control interface show you only the windows of the application or experiment with making specific browser windows full screen or set up several virtual desktops to segment your work.

Since there is no general way to enable this on OS X, you can look for lots of third party solutions to add a task bar functionality to the OS. I've always preferred the Mac way, but there are times when windows has a better workflow even for me - so I get your point and wish to not have to change the way you feel is best for you to work.

Since I don't have a silver bullet - if your windows are web browsers, you could get an app like fluid to make each web site look like a separate app, but you're still working in the dock / mission control / multiple window idiom and not the windows task bar idiom - so that might be like the proverbial "putting lipstick on a chicken"