Its actually pretty simple. On a hard disk, the first 64 sectors of the drive are unused, so what the manufacturers did was tagged those drives with an ID marker (HP did this method specifically, other manufacturers used the motherboard). So if you look online for a tool called HDD DMI, burn to a disc, boot off of it, then look on the bottom of your HP laptop / back of your computer for the hardware ID number, then when you boot off the disc, it'll tell you to type in that number. Punch it in, you can now use those discs with your machine. That's one way of doing it.If you have the licence key from the old machine (on the sticker-COA)..
The way it works is the key is 'non-transferable'...except...
This is checked against the hardware configuration to some degree from first activation or some such. I don't know how it works exactly...
The other thing you can do is look up a process called streamlining. Basically, you're breaking down the manufacturer discs, stripping out those ID checks and such, then reburn those discs. Streamlining is the process they actually use to make those discs, so if you're feeling fancy and clever, and you have some wacky off the wall drivers that Windows 7 won't auto-install, you can include those drivers with the OEM disc install, strip out stuff you don't need, add in software, etc, etc, etc. It's all pretty interesting, but extremely time consuming, and there's no automation for the process at all; you do it all by hand! Did I mention time consuming?
Yet another method you can do (this one is a bit more of a pain in the neck, but requires less expertise overall). Install Windows on that laptop, copy the hard drive in it's entirety over to the target computer's hard disk, and then boot off of it. It will fail to boot, but after that failed boot, you pop in your windows disc and run through Windows Repair mode. It skips the whole ID checking phase of it, and just reinstalls windows over itself with the proper driver preparation.
All of em are pretty straight forward you can do without much expertise, but if something breaks, that's when you need expertise to fix it =P
End of the day though, I strongly recommend a copy of Norton Ghost, or similar software. Get your machine installed just the way you want it, running perfectly, and then make a ghost of the hard drive on disc. It saves time overall when you encounter system failures, and will work as long as you don't replace your motherboard with something else (if you replace other hardware, it'll just install the new drivers once you get windows up and running again).