You can transfer it to DreamHost now:
Just make sure it’s unlocked, has your real contact info (not anonymized), and you have your authorization code.
Meanwhile, set up your fully hosted domain here and then follow these directions:
If your friend has your domain registered and hosted here, that’s not so easy. I believe it’s possible to transfer the domain registration the usualy way as outlined above. As for your domain content, DH generally prohibits moving hosted content from one account to another due to people setting one up under a promotion and then transferring it away.
You can either continue to run your domain under your friend’s account, or contact DreamHost Support to see if they can transfer it to your account.