[dayoungtx]

Is there a way to download my contacts from my phone to the cloud so that I can transfer them to another device in the future?

[Pete]

Yes, it happens automatically.

If you tap on a contact in your People list, you'll see a list of accounts at the top of the screen (under their name). The contact data will be attached to those accounts in the cloud.

If you log into Outlook.com, you'll see them listed in the People hub there.

[Ray Adams]

Or check contacts backup application.