Writer with no cost

You need to be able to offer them something. Either you need to be paying something or you need a site with high enough traffic someone might want to write for you in exchange for a mention and some links.

You can always set up a page on your site t invite others to submit a guest post together with some of the terms and conditions like the type of topics you are looking for, number of words, what they get back in return (a link back, etc) and such. If you need to see how other websites does this, you can always search for Submit guest post on the search engine and you'll see plenty of sites that do invite others to submit guest posts to. Also, if you are picky, tell them to propose some ideas and then pick the ones ou like.

That would be something that would help everyone. But like someone else told you need to share something too. Probably a BIO or why not the option to write freely. More or less a good writer will never come and do that for nothing. Your blog,website has to be too good so he can come and write for free or barter.

I've seen some webcomics handle this in a smart way - they plan in 2-3 weeks of guest content, so the artist can catch a break.
Maybe look for several people (friends, writers of the same niche, ...) who want to write an article or two for you and then use the extra time brainstorm!

Two main ways, I think ...

(i) Go to a site like Ezine Articles, use their inbuilt search facility to identify articles on the subject you're looking for, and just re-publish whatever you want (in accordance with the directory's terms of service, obviously!). They're free. That's what article directories are there for.

(You can also contact the writers of those articles and see what else they have available, which overlaps with the second way mentioned just below.)

(ii) Find someone who does "article marketing" and wants to offer you a guest post/syndicated article (you can get some pretty good quality writing that way, without paying - probably a better standard overall than Ezine Articles' "average"!).

In neither case will you get unique (previously unpublished) content, but that doesn't matter in the slightest. In both cases you can get a good article/post which your readers/visitors haven't read before, and that's presumably what you want? Some good content to publish? Shouldn't be too difficult. Thousands of people are doing this, every day of the week. As Amanda mentions above, you're effectively "paying" them with a link.

(For unique content, of course, you have to employ someone.)

Important note: stay away from any "services" like the recently penalized/de-indexed "My Blog Guest", whatever you do: Google is (understandably) fiercely penalizing the users of guest blogging "services" which it thinks are designed to manipulate its ranking algorithms!

Google the following: Keyword/nurl: guest post"
Replace Keyword with your niche keyword.

I often find it that the best solution for guest posting is a contest. Make the prize a banner on your blog for the winner and they will come!