What do I need to do to copy config from one ASA5505 to another?

Hi

i recommend to use a TFTP server to upload and download configurations,
otherwise, you can use its ASDM  to backup and restore configuration ..

go to tools, you can find there backup and restore configuration
or go to file and you can find save configuration to TFTP ,,, etc

or you can use CLI to copy running configuration to TFTP server
by
#copy run tftp:

then follow its CLI wizard .. very easy

Regards

Should I reset the replacement ASA back to it's original configuration first?

Copy Paste should work too. If you are using hyperterminal then you would have capture text option also.
The proper way which cisco recommends that you should make a tftp server & backup/restore files/IOS from there.

You can get free & very simple tftp server 'Cisco TFTP Server' by googling...

In the below link you will find comprehensive process to back/restore files from ASA/PIX appliances.

http://www.cisco.com/en/US/products/hw/vpndevc/ps2030/products_tech_note09186a008072142a.shtml

I hope it'll help you.

Regards

for sure clear all configuration on that ASA ..

Copy/paste do the same thing unless you dont miss anything during it... Just double check/compare configurations of both appliances. thats it.

Make sure to remove the 1st one from network before you connect new one on network if they have exactly same configurations...

I reset back to factory.   I use the copy/paste when I was in Hyperterm and many of the lines that were in the config I was copying showed up totally out of sequence.   I tried comparing the two and several of the options showed up in different places.   Isn't that going to cause an issue?