The short answer -- and this applies to Republican candidates too -- is: (a) Don't be as bad as the other guy, and (b) Be actively good on at least one important issue. As far as Democrats in particular are concerned, I have three specific pieces of advice:
1. Be good on the issues where the left is supposed to be good. When I was a lad, liberals were supposed to support peace and civil liberties (within the constraints, alas, of the Second Amendment Exception). These days, only one Democratic senator could bring himself to vote against the Patriot Act. John Kerry voted for the Patriot Act and the Iraq War, and since he wasn't willing to say he'd gotten them wrong he was reduced to complaining that Bush hadn't executed them properly. (Here's Kerry in March 2004: "The real problem with the Patriot Act is not the law, but the abuse of the law.") Say what you will about Ralph Nader's other views; on these issues he's pretty good. But he isn't a Democrat.
If you want me to see you as an alternative to the Republicans, be an actual alternative. Tell us you'll use the military to defend Americans, not for utopian schemes to remake the Middle East. Stand up against the steady encroachment of executive power. I'll understand if you're too frightened to oppose the war on drugs in toto, but you could at least allow the states more leeway to set less oppressive policies. In general, don't be afraid to condemn an ill-conceived intervention abroad, and don't forget that freedoms exist that do not involve the word "reproductive."
2. When you talk about tolerance, mean it. I'm glad to see you sticking up for gays and religious minorities. Don't wreck the effect by picking on smokers and gun owners. I don't want to be bossed around by the lifestyle police any more than I want to be bossed around by Pat Robertson.
"I don't hate smokers," you object; "I hate the cigarette companies!" OK: So take on tobacco subsidies, and go after the cartel created by the 1998 Master Settlement Agreement. Go after corporate welfare; go after corporate crime. But don't go after people who merely take risks you disapprove of.
3. Don't be a slave to the bureaucracy. Look, I don't expect you to turn into a libertarian. But there are ways to achieve progressive goals without expanding the federal government, and if you're willing to entertain enough of those ideas, you'll be more appealing than a "free-market" president who makes LBJ look thrifty. You could talk about the harm done by agriculture subsidies, by occupational licensing, by eminent domain, by the insane tangle of patent law. And no, I don't expect you to call for abolishing the welfare state -- but maybe you'd like to replace those top-heavy bureacracies with a negative income tax?
We have airline deregulation today because consumer groups, liberal politicians, and left-wing muckrakers wanted to break up the old airline cartel. But in the years since then, few Democratic leaders have emulated their example and looked for ways to shrink the state. In the presidential races, the two significant exceptions are Gary Hart and Jerry Brown, and of course they both lost. (When Brown ran in '92, he called for abolishing the Department of Education. Sounds a lot better than No Child Left Behind.)
So that's all I ask. When Republicans are bad on civil liberties and foreign policy, be an alternative. Extend your social tolerance to folks to the other side of the culture war. And if you can't be as pro-market as Hayek, try at least to be as pro-market as Jerry Brown.
Footnote: I say "he" even though the frontrunner is a "she" because there isn't a chance in hell that Hillary will do any of these things. Not that I expect her chief rivals to be much better.