I’m new to this web hosting thing so I probably have an easy question here

I read that the best thing to do is to register the domains with an domain registar and to host your website with an hosting company. So to separate these two.

So I registered a few domains with namecheap.com and I’m looking for a good shared-hosting solution right now. I would like to be able to run more than one site on the same account.

Now I don’t really understand how to forward these domains to the hosting company. The only way I’m familiar with is the URL forwarding. But is this the best way to do it?
I know there is DNS forwrarding (where I’m not familiar with) but can this be used with shared-hosting or is this only for dedicated and virtual servers?

So could someone explain how this thing exactly works. Let’s say I find a hosting company and I register with them. I create a few folders with websites. Now how do I forward these domains to the (shared)hosting?

And as I said I would like to run more than one site, but will this cause any problems with the search engines?

Thank you