Please tell us which dbms you're using in the future, because a lot of this is slightly different from one to another.
In postgresql you can do this one of several ways.
from a command prompt:
pg_dump dbname -t tablename >somefile
vi somefile
(change the table name to the new table name here)
psql dbname -e <somefile
Is the "around the back way" and allows you to port your table to different databases on different machines easily.
If the table doesnt' exist this works fine. If it does, then edit somefile so that the table deletion/creation parts are gone and only the connect and copy from stdin are still there.
In SQL you can do it one of two ways. If the destination table does NOT exist, then:
select * into newtable from oldtable [optional where clause here.]
if the table exists, you must be more explicit:
insert dest (column1, column2, ... columnn) (select column1, column2, ... columnn from source);