On a mac, your MySQL installation is located in:
/usr/local/mysql/
This is the folder structure:
$ ls -lah /usr/local/mysql/
total 64
drwxr-xr-x 16 root wheel 544B Nov 13 15:54 .
drwxrwxr-x 27 root admin 918B Nov 24 11:42 ..
-rw-r--r-- 1 root wheel 18K Nov 13 15:47 COPYING
-rw-r--r-- 1 root wheel 7.2K Nov 13 15:47 INSTALL-BINARY
-rw-r--r-- 1 root wheel 2.5K Nov 13 15:47 README
drwxr-xr-x 46 root wheel 1.5K Nov 13 15:54 bin
drwxr-xr-x 18 _mysql wheel 612B Apr 27 13:37 data
drwxr-xr-x 6 root wheel 204B Nov 13 15:54 docs
drwxr-xr-x 37 root wheel 1.2K Nov 13 15:54 include
drwxr-xr-x 12 root wheel 408B Nov 23 08:58 lib
drwxr-xr-x 5 root wheel 170B Apr 25 06:48 man
drwxr-xr-x 19 root wheel 646B Nov 23 08:58 mysql-test
drwxr-xr-x 3 root wheel 102B Nov 13 15:54 scripts
drwxr-xr-x 32 root wheel 1.1K Nov 13 15:54 share
drwxr-xr-x 28 root wheel 952B Nov 13 15:54 sql-bench
drwxr-xr-x 16 root wheel 544B Nov 13 15:54 support-files
You probably want to copy all of it to your local disk, then install MySQL from a disk image (DMG), backup the installed data folder, copy your backed up data folder contents into /usr/local/mysql/data, permission the folder to mysql, start mysqld and do an mysql_upgrade.
install mysql server from DMG... then...
sudo mv /usr/local/mysql/data /usr/local/mysql/data_ORIG
sudo cp /mybackupfolder/mysql/data /usr/local/mysql/data
sudo chown -Rf mysql:wheel /usr/local/mysql/data
sudo su -
nohup /usr/local/mysql/bin/mysqld_safe &
exit
/usr/local/mysql/bin/mysql_upgrade -u root -p
# read output
*Note: if you have a my.cnf, mv it to /etc/my.cnf.ORIG before you start mysqld.