You enable Apache in the Sharing prefpane. Check "Web sharing" and your web server is running.

To activate PHP you'll need to edit /etc/apache2/httpd.conf in Terminal.app. This require root access. Nano is a very accessible command-line editor.
sudo nano /etc/apache2/httpd.conf
Find the line (you can press ctrl + W to start searching in Nano):
#LoadModule php5_module libexec/apache2/libphp5.so
and uncomment it. Next find the line
#Include /private/etc/apache2/extra/httpd-vhosts.conf
and uncomment that as well to enable virtual hosts support.
Save the file and exit Nano by pressing ctrl + X, then confirming the changes by pressing Y(es).
You can now edit your virtual hosts in the file /etc/apache2/extra/httpd-vhosts.conf
sudo nano /etc/apache2/extra/httpd-vhosts.conf
To install MySQL, download the installer from the MySQL website (64bit installer should be ok). Follow the instructions to install it.
Finally, to configure PHP for MySQL, copy the php.ini:
sudo cp /etc/php.ini.default /etc/php.ini
Now edit php.ini (again root access required) and replace any reference to /var/mysql/mysql.sock with /tmp/mysql.sock (the default location of the MySQL socket after running the installer). There probably are about 3 references to that location.
Finally, restart Apache for the new configuration to take effect:
sudo apachectl restart
Alternatively you can restart Apache by toggling it off and on in the Sharing prefpane.
Done.