I want an amendment to end lifetime tenure for Supreme Court judges.That's a great question.
What should I and people like me do to get such an amendment ratified? Who are the first people we need to convince?
First, on the substance...I've written about this before, and wound up in the mushy middle. Apologies for the laziness, but if you click through there you can find links to arguments from Matt Yglesias and James Fallows (for) and John Sides (against) as well as some relevant research.
Now, to the question. I wish I knew the issue emergence literature better than I do, but I'll comment anyway, and perhaps someone who knows more than I can chime in. Mostly, this is speculative, but it's a fun question, so I'm going to talk about it a fair amount. But the first thing I'd say is...you're talking about a very, very, tall order. Constitutional amendments are extremely hard to get enacted; you're talking about really just 11 Amendments (#s 16-26) that were produced through the normal political process. Still, those did happen!
Anyway, there are a couple things you want. Ideally, you would want a set of Congressional sponsors: at least one Democrat and one Republican from each House of Congress -- even better (and somewhat more likely to happen) if they're on the Judiciary Committee, and even better if they're the chair and ranking members of the relevant subcommittees. That's the gold standard. How does that happen? Members of Congress are always looking for good ideas to champion, because it produces favorable publicity. So the trick is to get the idea out to where they (or their legislative staff) would notice it. Get it mentioned frequently in high-profile blogs, get someone at a think tank interested enough to hold an event around it, get an op-ed in the New York Times or the Washington Post.
How do you do raise the profile of an issue if you're just a regular interested citizen without connections or pull? It's not easy! But it's not entirely impossible. Bloggers do read their comments and email (especially, I'd guess, those who get manageable numbers). Bloggers are also -- and this I'm sure applies to all of us -- looking for easy ideas for items. Think of good hooks; for this issue, any Justice's birthday is a hook, as would be the anniversary of when they were sworn in, especially those who have been around for a while.
Given that a Constitutional amendment is better-off it it's bipartisan, on this kind of issue my guess would be that the best way to proceed is to try to get elite consensus around the issue; you're better off with David Brooks and Thomas Friedman than you are with your local House candidate. On more partisan issues, however, that's almost completely reversed. If you want, say, a public option added to ACA, then your best bet is to do whatever you can to push Democrats running for the House or Senate to support that issue. That takes personal activism, or even better group activism. A lot of House campaigns are pretty small-scale; if you (and a group of friends) can devote a few dozen hours to a House candidate in a contested primary, odds are you'll be in a position to at least somewhat influence the issue positions the candidate takes. Of course, there are limits to that (it's unlikely that you'll flip the candidate's strongly-held positions, or those that are considered important for election -- but there are plenty of issues in which neither the candidate nor most voters care a whole lot). Now, there is of course limited effectiveness in pushing one House district to your views, but the next step is to organize people in other districts to do the same thing...bottom-up, or middle-up-and-down, strategies are certainly viable on many issues. I should mention: yet another method would be to organize a formal interest group. That's a lot easier on some issues than others, but individual citizens can start up groups, add members, secure funding, and then raise the profile of the issue that way.
But not, I would guess, something such as a Court term limit. That one happens, if it does happen, top-down. And my guess is that only a major increase in lifespan would make it a politically viable idea.