How do you deal with copyright infringement notification?

Recently we received a notice from a reputed motion pictures company asking us to close the classifieds section that had to with digital media? We complied with their notifications and had to close/delete that section?

Is this how it works?

If you have copyrighted movies/shows for download they are able to do that and it's best to comply. Otherwise you could be taken to court or the entire site shut down.

This should help: Wikipedia: Copyright infringement

For the most part, if you comply with their demands, then you should be fine. If they have to repeatedly contact you, one of the contacts will likely be a subpoena to court and then you get to experience paying a lot of money and likely losing the battle

Now, you must also watch out for those who claim its theirs without proof, a lot of people like that are out there.

yes, there is a template for responding back to them. You can ask them for the ownership proof and upon receiving the same, you may have to comply to them unless you want your site to be forfeited.

I would ignore it unless I had actually committed copyright infrindgement. There are a ton of people out there that try to get you to remove content that is ranking nicely just so they can swoop in and overtake your spot.

Well, if your members were offering/trading copyrighted materials, then you were in a bad position and it's good you decided to comply. The best idea is to make sure you're not allowing for anything 'weird' so that you don't have to deal with such an issue from the get go

SEO is right. I also think people would mostly take advantage out of it, to swap places with you.

Yes you are right , and why will you use the copyrighted materials, may you can do some research or use your own material.