How do I export photos on my iPhone 4 to an external hard drive?

You can use an app like Phone Disk so that your iPhone appears as a usb device on the Mac. Then just copy the pictures folder and paste it into you external drive. The app is not free, though.

Another option is to use a PC. Windows will see the iPhone as a camera in "My Computer" and you can copy the DCIM folder from there into the external drive. This is a free option.

A third option is to use Dropbox, but if you have tons of photos, that might not be enough and it might be a hassle to upload them all from the phone.

Maybe someone else has a better suggestion out there?

The proper way is to

1) remove excess/unused/old data from your mac, freeing up space

2) perform a back up of the mac

3) off load anything you don't use regularly to a second external drive which will allow you access if necessary.

4) sync as usual