Normally what the sites offer is a free trial period of say three days, or the opportunity to create a free profile.
Some sites will then allow you to see the content of those messages, others won’t. This means that unless the person contacting you sends you a phone number, or email address (some sites automatically remove these) you won’t be able to contact them until you pay for your membership.
If there is no completely free dating site, is there a point in signing up to one of the free offers? This is because you can check out the members on the site for free to see if there are some interesting ones, send them a winkie (or similar), and see if there is mutual interest. We have to say, of course, that one of the so-called best "freedatingsites" is Love Again.