We have several users running on old hardware and old browsers.
What would be the best way to get them to upgrade to a newer web browser, without nagging users with a newer web browser.
If it's not a page that is mandatory to be seen even with an old browser, and you don't mind having a part of the visitors leaving, you could just develop it using latest technology and let the user see the need for updating their browser first-hand. Of course, this is not viable in anything business-like, but for personal pages or for sites that simply require some new feature to work (as strange as that is!), it should be fine.
The courteous thing would be to remind the user that in order to see the page fully, a modern browser is called for. Eventually this will drive the masses to upgrade to modern browsers, and thus make the new features more reliable for the developer to use in more conservative pages (corporate, retail, banks, etc).
This should fit your requirements. Users of modern browsers will see the page as intended, and users of obsolete browsers will see that they need to upgrade.
I don't think you can - look at Microsoft's attempts to get Silverlight pushed out to everyone, even as a plugin it failed to get more than 60% or so. If they cannot persuade everyone (via marketing, hype, and web pages with "you must install to see this" then I'm not sure you're going to have much success.
I think the best way is to let the natural evolution take its course, one day all the old browsers will have enough of a market share that you can safely ignore them - and keep an eye on your log statistics to see which browsers people are using when they visit your sites. Choose a percentage below which you will no longer support that browser. For these people you can display a "you need to upgrade" page. Alternatively, provide them with a very basic functionality page containing no advanced features, so they can work with a subset of functionality and put your nag reminder at the top of it.
The rest of the time, just remember that you will always be chasing a older version, if a new browser technology appears today, it won't have critical mass to be usable in production for a good couple of years.