If the old and new appliances are running the same version, it should be very easy.
One of the tricks with the Firewall command line is that the output of a 'query' command is essentially in the same format as the input for that command - all it is missing is the "cf" porttion.
There are various network object types (ipaddr, subnet, host, domain, netgroup, etc...).
To create an export of the IPAddr objects, for example, run the following command:-
cf ipaddr query > ipaddr.txt
This will create the file ipaddr.txt in your home directory. Use WinSCP or a similar SCP tool to download that file from the source firewall to your PC.
Then copy the file to the username's home directory on the new firewall appliance.
The only real consideration to bare in mind is that a brand new Firewall installation contains a couple of network object definitions by default (Firewall & localhost spring to mind), so before you do anything else open the text file and remove the entries which already exist on the destination Firewall - otherwise when you try to import them the process will fail.
With the edited file present on the new Firewall, run the following command:-
cf -f ipaddr.txt
Roughly translated - open the file "ipaddr.txt" and use it as the input for the "cf" command.
The time it takes the import to complete is going to be dependent on the number of objects in the text file, but it shouldn't take too long. If you are returned to the command prompt without seeing any errors you should be good to go!
Either run "cf ipaddr query" on the new Firewall or take a look at the network objects screen and you should find they are all there
You can then repeat this exercise for the different network object types. Leave the netgroups until last, of course, as they will need to reference existing objects.
If your new Firewall is running a different version to the old one then it is wise to check that the format hasn't changed. v6 object definitions were different to v7, but I think v7 & v8 are pretty much the same. If you are going from a v6 (G2) appliance then you'll need to do a bit of search/replace on the text file before you try to import it.
I have personally found the easiest way of identifying the differences is to create a new object manually on the new Firewall and then use the "cf <object-type> query" command to see what it looks like.
Hope that helps you.
Phil has a pretty good summary. I do want to mention that the syntax on the rules has changed dramatically from v7 to v8, but I agree the objects should be very similar.
If possible, your best bet is to make sure both firewalls are at the same version and do a full configuration restore. It will pull everything over. You would then need to change a few things like IP addresses, licensing, etc, but it should be a bit easier than pulling everything over manually.