You need to dump the database data and table structures into a file. Then read that file into MySQL on the new server. I've never dumped using the command line, but check the mysql pages for detailed info and which options to use. To read back in, just use '<' or 'source' from the shell.
The most common use of mysqldump is probably for making a backup of an entire database:
shell> mysqldump --opt db_name > backup-file.sql
You can read the dump file back into the server like this:
shell> mysql db_name < backup-file.sql
Or like this:
shell> mysql -e "source /path-to-backup/backup-file.sql" db_name
mysqldump should already be included. Make sure the MySQL bin directory is in your PATH environment variable. For bash, I believe the command to set is 'export'...: export PATH=$PATH:/pathto/mysqlbin/
Or try running the command from the bin directory.