Moving MySQL database from one machine to another and remotely accessing dbs?

[Martin Waller <martinej.waller@ntlworld.com>]

Hi,

I'm using MySQL 4.1 on Etch and have a database (that I created) on 
another machine (still Sarge) that I want to transfer to the other 
before upgrading to etch on that machine also. Where should I look to 
find out how to do this?  Is it just a matter of locating the database 
and copying or is it more subtle? Are there any security considerations?

On the security note, I'd also like to be able to access the database 
from other machines but am unable as by default remote access to the 
server isn't allowed - again, where should I be looking for information 
on how to change this?

The MySQL docs are pretty daunting for a database newby, and I was 
hoping there'd be some debian-specific documentation somewhere...

Thanks if anyone can help point me to the relevant information source,

Martin