There are a few different approaches to take here but it sounds like the best solution for your situation would be to use the "External Form" block. Check out YOURSITE/concrete/blocks/external_form/forms/ for an example of how it works. To add your own, copy that "forms" directory to:
YOURSITE/blocks/external_form/

(so you're copying it to OUTSIDE of the /concrete/ directory)
Then change the name of the test_form.php file in that folder AND in the "controllers" subfolder to something else (should be the same for both of those files, but different from "test_form"). Now you can modify that to your liking.

When you're done you can add the form to a page by adding the "External Form" block and choosing the form you made from the list.

-Jordan

Thanks Jordan,

I actually thought of a solution just after I posted this, I just simply pointed the action field to the current page where the form is and created the validation in the theme file for that page.

Hello!
I have two things which are not clear to me: the action of the form, and how to validate fields..
How can I create required fields for example?

It's been a while since I wrote this response, and since then I've actually changed my mind about the external_form block -- it has a number of annoying limitations and quirks which make it very difficult to use a lot of the time (in my experience anyway).

What I do instead now is just create a block that has a form in it. I've put up a simple example of a contact form block, which shows things like how to handle the action of the form, and how to validate fields. The code is available here:

https://github.com/jordanlev/c5_custom_contact_form...