sync an existing WP site with local site?

I have a blog set up by my host and I have my development site set up on my PC. They are different because the host set up the live site and I set up the local site.

I would like to be able to synchronise my local and live sites. I have tried creating a database with the same name, user and pw on my PC using the details from the wp-config file on the live site but that doesn’t work. I also copied the wp-config file from my live site to my local site. That didn’t work.

Many thanks

Martin