Many things that might be said here. Two classes of drive 1) External USB, 2) Internal sata with a custom port to the motherboard.
1) You can set up profiles and more on USB these days (might even have a measure of DLC but I am not sure what goes there). Equally I am not sure if you can do split partitions a la the Wii (kick 32 gigs to the profile side of things and have another to hold games for xexmenu/FSD and files for dashlaunch)- get a thumbdrive of a couple of gigs and you are sorted there though.
2) Internal is still sata inside the case. However 3.5 inch or 2.5 inch?
3.5 and it gets potentially tricky unless you power it externally (3.5 usually wants 12V which you can get if you solder inside the 360 but it is not the easiest mod- the internal sata is laptop sata which does not have 12V).
2.5 inch and you are going to want a case unless you feel like soldering a lot . Most of the Chinese random computery parts sites will do them (
http://dx.com/p/hdd-hard-disk-drive-case-for-xbox-360-black-30826 seems to be the slightly more expensive black ones) but personally I have taken to going to shops as old 20 gig drives are often about the same price and I do not have to wait for shipping from China.
I will note some of the terabyte drives are taller than the standard 2.5 inch drives which means you get to slice up the inside the case to make it fit or just rip the adapter plug out and stick the drive somewhere else.
Software side is easy- you just need to format it. The xbox itself should handle it, if you are playing on the PC then Xplorer360 should have the functionality but hddhackr (necessary for non RGH/JTAG hacks) if not.
If you are reading up on a guide to do it normally and it mentions hdss.bin ignore it as that is for when you want to make one that works in a regular 360.
The only minor troubles are the hard drive is where the xbox backwards compatibility emulator is stored and avatars/kinect if you care about such things, if you have a JTAG/RGH box this is not a problem as you can just write the files to the drive (probably at the xplorer360 stage but FTP should be able to handle it otherwise) and you are probably going to want to write the hacked versions that boot more games, boot homebrew and generally do what hacked versions of programs do. If you do not care about xbox BC (and frankly I still say get an original xbox if you are after original xbox goodness and a nice emulator/video player to boot) then no worries here.
I believe there is even a 360 side homebrew program to add it in these days but the FTP/xplorer360 method is what I opt for.
Avatars/kinect is usually a variation on get the same update (very important that) as the version your JTAG/RGH box is pretending to be and extract it to a USB thumbdrive, rename folders to get around update preventions and run it. It will then add it in.
More detail
http://team-xecuter.com/forums/showthread.php?t=90631
Or others 
