I have just bought my own PS3, after using my brothers for the last few months. I was wondering if I could copy/transfer my profile and saved game data from his PS3 to my new one and if so how to go about doing it. Also, would it have any effect to his PS3 as he has only agreed to let me try it if I know what I'm doing. Can this wipe his PS3? Can I copy my profile and saved data to my PS3? I haven't backed any of it up but both PS3s are fully working.
You have a couple of options:
Create a backup of your brother's PS3 using the Backup Utility and restore the same backup on your new PS3. This won't wipe any data off your brother's PS3 and will transfer most of the data on your PS3, excluding some data (like copy-protected saves and media). This will copy both your profiles to your new system, but you can delete your brother's data afterwards.
Copy just the saves. On you brother's PS3, plug a storage device like a thumb-drive, go to your profile and open the Game Save Utility under the Game category. You can choose to copy individual saves or all the saves at once to your storage device, then plug it into your new machine and copy them to your local profile. Please note that you should probably log to the same PSN account you've used on your brother's machine (if you had one) or otherwise the saves may be unusable. Again, copy-protected saves may not be available to transfer.
Copying your profile is simple because profiles are stored on Sony's servers. Just log into your new PS3 with your PSN account and your profile and trophy data should be available. Make sure to sync trophies on your brother's PS3 first.
Saved games are different. As JohnoBoy says, you can use the backup utility and/or a USB drive to copy some save files, but others are copy-protected and cannot be copied this way.
The only way to copy copy-protected save files is to use the cloud service offered by PSN+. Copy-protected saves will be inaccessible for 24 hours after copying them to the cloud, but after this you will be able to download them to your account on your new PS3.
As of right now (November 13th 2012) you can get a 30 day free trial of PSN+ if you "like" them on Facebook. It's only valid for Sony Europe countries (EU/Australia) though. I'm not sure if there is anything similar for the US running at the moment.