Hello Stephen,
you can follow some steps:
a) setup the eBGP session to the new provider
advertise your IP prefixes to this neighbor
Use a public looking glass to verify the correct propagation of your advertisements or have the new provider's feedback
b) verify you are receiving a BGP full table from the new provider just use sh ip bgp summary and compare the number of prefixes receveid by the old and by the new provider
they don't need to match but to be of the same order
note: to do this you need to verify that you have at least 100 MB of free memory on your router to hold all the prefixes you receive in the new eBGP session
c) after all checks you can provide preference to the new provider for outgoing traffic
note: until you have the eBGP session with the old provider you have limited influence on the return path you can just prepend your own AS number in your advertisements to old provider
Hope to help
Giuseppe