Positioning of quotation marks in conjunction will full stops

[SurreyGuy]

When writing an article that contains a few continuous quotes, where does one put the full stops at the end of paragraphs in relation to the quotation marks?

This is how I have written it, but someone told me that my positioning of full stops/quotation marks is incorrect -

Dave said, "When I first saw the dog I wasn't sure what to do, so I just froze. However, when I thought about it, I relaised that that was the worse thing I could have done".

"Once I had stopped, the dog seemed to calm down and was extremeley friendly towards me. I wish I had stood still in the first place".

[mallam]

The rot goes right to the top, you see.