Most podcasts like you're describing start by using the audiences of their guests. This makes it tricky, because you're effectively asking someone to come on your show to leverage their audience for your growth.
That's still a value proposition for the guest, however, because it's back links, external content, and more credibility to their own audience. (Assuming they don't already have a podcast.)
Aside from leveraging your guests' platforms, you can also use standard marketing tactics to create your own network: guest blog, get active in the community, and do whatever else you can to generate backlinks and buzz.
I'd be happy to go over strategies that have worked for me and my clients if you need a starting point. Just let me know.
I know several people who publish their own podcast series of interviews. And publishing written interviews is something I've looked into as a possible project.
Seems to me that you'll get nowhere without first having either a chicken or an egg. Doesn't matter which; but you'll need some advantage, some element in place in order to attract the missing elements.
An established audience would attract interviewees. Don't have an audience? Then a scheduled guest list might give you something to market pre-launch, and it might give people a reason to pencil you into their calendars and subscribe to a newsletter or like or follow you on social media.
Can't convince star entrepreneurs to commit to interviews because they see zero audience and don't know who you are? Then either get the audience first or focus on branding. If you show up with the right brand – whether that's you personally, impressive backers, or a promising platform – then doors may open for you even before the audience is in place.
When you're ready to think about naming your project, branding, or domains, maybe I can help.
This is an excellent question and one I often hear for any type of product or service in need of attention. I've successfully built both profit and non-profit businesses using grassroots methodology. Here is what I suggest as a great low-budget starting point.
Your project is very similar to the book "Think and Grow Rich." Your audience will be best built using your interviewee as the anchor. Anchor meaning, the reason people are tuning in to listen or download your podcast. If you can interview someone everyone knows like Mark Cuban or Damon John, I'm sure you'll be widely successful from show #1. However, if they are unavailable look for others people to interview who have a footprint larger than yours. Who is the most famous entrepreneur you know? Now, who is the most famous entrepreneur your 5 closest friends know? You see what I'm getting at? Find someone who brings an audience with them.
If the person you interview tells their followers and fans, and you tell your followers and fans, your initial show will be awesome. As you build more great interviews, people will begin to tune into your podcast just to see who else you might have on it. Be sure to send an invitation to the local business newspaper and to bloggers who might listen in and then write about your show.
Be sure to post new podcasts often and make wise interview choices with great interview questions. You may also want to ask the general public the questions they want you to ask.
Build your podcast in this grassroots method and you'll have all the audience members you need progressively. Good luck. Contact me at any time with any follow-up questions.
I'd agree with the other answers here that in the beginning, your best bet will be to leverage the audience of your guests.
There's a trick to doing it properly. Instead of just sending them a link to tweet or letting them know when the episode is live, it's important to make it dead simple for them to share.
You can create sound bites and upload it to Soundcloud and it'll play directly in the twitter feed. You can create custom graphics for them to share on social media. Get creative here.
Another thing you can do is launch a giveaway to promote the podcast. Entry couldbe something like subscribing and leaving a comment on a specific episode.
Some podcast platforms (see more here: https://www.kyleads.com/blog/podcast-hosting/) also have built in directories that help distribute your podcast further.
You may even consider using cheap social ads to build up that engagement and social proof. Social ads paired with a landing page (see more here: https://www.kyleads.com/learn/landing-pages/builder-software/) that focuses on either capturing email subscribers or podcast subscriptions would be a good investment. You want to try to get over that initial hump of about 1,000 regular listeners.
From there you may start to see compounding effects.
Hope this helps.