When it comes to print-on-demand (POD) publishing without upfront costs, the only publisher I have worked with directly myself is Lulu. I didn't use any of their add-on publishing services but formatted and uploaded my own file and worked with their free cover creator tool. I haven't sold many copies of my book on their site, but I've had some copies printed and mailed to me, it's been a nice gift to share with friends. I've also sold copies here and there at readings and other events. It was completely free for me to publish my book on Lulu; I only paid for the individual copies of my book that I had printed.
I know a couple people who have used Blurb to self-publish POD books, and in both cases, it was for one of a kind photo books. Both friends didn't pay for additional help but did all the design and formatting work themselves.
The other POD option that I see mostly commonly used is CreateSpace (which is owned by Amazon), and I think this is for two main reasons: the ease of using Amazon's tools, and the big market share that Amazon maintains. Here is a great tutorial from Joel Friedlander about how to self-publish your book on CreateSpace.
When it comes to e-books, the biggest game in town is Amazon's Kindle Direct Publishing. I have published here, and it's relatively easy to format and upload your file. Here is the beginning of Amazon's tutorial about how to do it.
Smashwords is also a popular e-book platform that's free for authors to use, and they've posted an interesting article about why they don't recommend KDP and Kindle Unlimited. I have a book up on Smashwords that's free to download, courtesy of a small publisher called NAP.
If you need a clickable table of contents for your e-book, by all means read Richard Levesque's tutorial on how to format your table of contents. This helped me enormously!
You may also want to experiment with the templates on Canva.com to help you make free book covers for your e-books.
I find all of the freelance design help I need to publish my books on Fiverr.com. You can find all sorts of services on Fiverr, including help with formatting your book, proofreading, marketing, and more.
Kindlepreneur is a creative website for ideas on e-publishing, and here's an interesting post with ideas on how to get the best deal on Fiverr for book cover design.
The best cover designer I know is Sandra of tbwcovers.com. She used to make and sell book covers on Fiverr but expanded her business to create her own site. Her work is professional, high quality, and great looking. She is also an author herself and very helpful and understanding to work with.
If you want to offer books or other products for sale on your website, the blogger Leslie Samuel has an interesting article comparing payment processors PayPal, Gumroad, and Stripe.
The "Writer Beware" section on self-publishing on the Science Fiction Writers of America website gives a great overview of modes of self-publishing and how to avoid scams.
The reddit community on self-publishing is a good place to browse and read about other writers' experiences with self-publishing and to ask questions.
Jane Friedman is an editor, publisher, and teacher with some very interesting resources on her website.
If you're interested in the history of self-publishing, here's a timeline put together by Poets & Writers magazine.