Medar,
telnet/ssh to your host
type: mysqldump -u<dbuser> -p <databasename> > dumpfilename.dmp
then enter your dbpassword at the prompt
when that's done, type gzip dumpfilename.dmp
then you can ftp that file (in binary mode) to your new host... telnet/ssh there and:
type gunzip dumpfilename.dmp.gz
mysql -u<dbuser> -p <databasename> < dumpfilename.dmp
enter your dbpassword at the prompt.
this will load the entire database (all tables and data...)
I do this with my site all the time (120+MB) and it runs no problem...
If you have any other questions, feel free to ask!