Restore After Changing Table Structures

Hello List!

We're working on restructuring some of our tables in our databases
(removing, renaming, &/or adding columns to tables), & adding tables to the
database, etc. - and we have a database FULL of info that we want to restore
this database with once the updates are done; however, I know that I cannot
simply do a 'Restore' to my database if I'm removing/renaming columns, etc
since some of the column names that existed in the database that we did the
Backup on will not exist in the one that we attempt to do the Restore on...

What is the most efficient way to copy/restore data from my old database
into my new one taking these changes into consideration? (pgAdmin sure does
spoil us, doesn't it?! ;))

We're running Postgres version 8.0.8.

Thanks in advance for your time and help with this!!
-Jeanna