How to restore mysql databases from /var/lib/mysql/user_database/ files only

Hi,
as the title asks. I recenlty had a hardrive failure and luckliy I can still access certian directories on this drive. I can still access the /var/lib/mysql/ direcoty which holds all the users databases and have backed all these up using tar.

Now what I need to know is how do you restore these database files to another server? I tiried simply untar'ing one of these to a new server - for one single user - and it stuffed up Mysql - it went offline.

So how can I get these database files to fully work on a new server? Please any help would be greatly appreciated.