I'm switching mobile phone service and I want to port over my contacts
If you're just after the contacts, that should be easy as 1-2-3:


open the contacts app, tap the menu, chose "Export to SDCard"
copy the resulting file (in most cases named something like 0001.vcf over to the new phone
on the new phone, same as in 1. – just chose to "Import from SDCard"


Of course, there are several more alternatives – depending on your preferences:


if you've synchronized your contacts with Google (or some other cloud service), they should automatically be synced to your new device as soon as you connect it with your account
plenty of backup/restore apps are available to assist you, some even specific to contacts
more information might be found in our backup tag-wiki