Have, have had, has, has had, had, had had

Can someone give me a simple explanation the differences in the use of words/word groups? Thanks.

I have a dog today.
I have had a dog, but I don't anymore.
He has a dog today.
He has had a dog, but he doesn't anymore.
I had a dog yesterday.
I had had a dog, but I don't anymore.

That's not that helpful... But it's a start.

Call Uriel, quick!