Without knowing the exact spec on the older laptop, you have to do a little research. There's two ways to do it: transferring the physical hard drive and doing data transfer. Both will take a fair bit of time, and if you're not familiar with Macs, the data transfer is by far the easier way to do it. I'll explain how to do it data transfer style, then I'll tell you about physically moving the drive.
Before you do any of this, just to be safe, make backups of both systems. Don't know how? Plug in a big enough USB drive, and use "time machine." Google "time machine macos" and find out all you need to know.
Data transfer mode: You want
- Both macs shut down cleanly (Apple menu -> Shutdown)
- MacOS operating system DVD that's compatible with the new Mac (perhaps the one that came with it)
- Firewire cable (see below)
First, get both laptops in a room and both on power supplies (can't do it on battery). You will want a firewire cable that fits both laptops. The newer one almost certainly has Firewire 800. The older one, depending on how old, may have only Firewire 400. The cables are different. Any Best Buy or Microcenter or Frys will have a Firewire 800-400 cable, or a Firewire 800-800 cable. Figure out what you need and go buy it. Even if you get ripped off at Best Buy, the most you'll pay is about $30 for the cable, which is totally a worthwhile investment when you see how easy this is. Here's what a firewire 400 port looks like: http://img4.realsimple.com/images/0809/firewire-400-port_300.jpg. Here's what a firewire 800 port looks like: http://img4.realsimple.com/images/0809/firewire-800-port_300.jpg.
Once you've figured out the cable you need, boot the old mac up into "target mode." (see the Apple KB in "sources" below) Connect the Firewire cable between the two macs. The new mac will see the old one like it's an external hard drive. This is a really neat trick.
Boot the new Mac and put the Mac OS X DVD in it. Act like you're going to reinstall MacOS X. Reformat the hard drive, do whatever you normally would do if you were going to reinstall the laptop. At some point it will ask you "Do you want to move your files and applications from another Mac?" Say Yes. Choose Firewire. Go make coffee. Have a sandwich. Play foosball. It will probably take a couple hours.
When it's done, you will have a perfectly new, reformatted Mac with all the files from the old Mac, all the applications from the old Mac, and all the settings from the old Mac (e.g., wireless networks and so on). I've done this many times and it works like a charm.
Caveats: there are several kinds of software that install kernel extensions. They often will not transfer cleanly this way: Parallels, VMWare, Cisco's VPN client. These are the ones I've run into. You just reinstall them. All their settings and data -will- be moved through the data transfer.
OK, after reading all that and seeing how easy it is, you still think you want to move hard drives, do you? This is not for the faint of heart. I have done this a few times, too. You need a zillion different tiny screwdrivers and usually some itty bitty torx screwdrivers. This isn't a clunky piece of Dell crap, this is a precision engineered piece of equipment, with VERY small tolerances. Last time I replaced a hard drive on a Macbook by myself, I had to take out 21 different screws, no more than 4 of which were the same. You have to remember what goes where and not lose them. And you're going to do this on TWO different laptops. It took me an hour the first time I did it, because I was scared to death to screw up the $2500 laptop my employer had bought me. This will be very fiddly and require a lot of precision and patience.
Before you embark on this adventure, you have to figure out if the hard drives are compatible. Go to the Apple menu on each one. Click "About this Mac." On the window that appears, click "More info..." Now you get the full hardware inventory of the system. Look under ATA and Serial-ATA on both. If one has an ATA hard drive, and the other has Serial-ATA, you're done--You can't move the hard drive from one to the other so your only option will be the data transfer option above. If they both have Serial-ATA, you can think about moving it from one chassis to the other.
Here's some instructions at ExtremeTech: http://www.extremetech.com/article2/0,2845,2119528,00.asp. Notice that there are 31 slides. Good luck. Notice also that these are for modern Macbook Pros. Since you didn't give a precise description of the old one, I can't point you to instructions for it. Needless to say, the instructions are NOT the same. Each generation has its own layout and arrangement.
Good luck.