There is no single way of getting publicity, no silver bullet. It's a snowball effect, several small pebbles thrown in the right spot at the right time will cause an avalanche.
And yes, you should post on HN first.
But failing that or having a less revolutionary product, I would highly recommend blogging, whatever your start-up you must have interesting insights and tips about your industry that you could share.
If your not committed to regular, high quality blogging and for many founders that doesn't fit into their skill-sets then think about creating one time big research reports that would shake the industry or provide some highly valuable new information.
Blogging and reports are perfect for a start-up because there is virtually no cash cost, so if your bootstrapping or just playing it smart then these are my top two.
This is something that requires significant creativity to do well. One of the biggest problems today is not getting your message out there - we have more channels than ever before for that - but rather getting your signal-to-noise ratio high enough that you're not lost in the background.
A good trick is simply to always be making connections about the brand. Most of them will have a small overall contribution to brand awareness, but they can be meaningful in aggregate and there will be a few contacts which generate a large payoff.
2. Develop a list of media contacts.
3. Follow what the contacts on your list write about.
4. Look for connections between their stories and your stories.
5. When you find these connections, pitch the story.
If you've done steps 1-4 correctly, you'll find step 5 easy.
And yes, word of mouth. You'll find the first users among your friends, HN and reddit.
What is the process of getting publicity for a startup without any connections or investors to help?
users are needed first
However, if you want a TON of publicity then just do something that will get you noticed for instance, just look at how Richard Branson does publicity for some of his brands - http://www.businessday.com.au/small-business/smallbiz-market...
Likewise, if you want a users then there are loads of methods of doing it and although you don't want us to mention it "word of mouth" is the BEST form of publicity & user signups
Nevertheless, if you can clarify which one you would like answering I'll gladly help and I'm sure the rest of HN wouldn't mind helping either. Moreover, if you can mention what your startup does or even the industry its in, we can be a little more specific because, there's no point telling you to reach out of X, Y and Z if they won't get you the users you need :)