There are already lots of threads about this issue and some guides floating the web explaining in detail what steps to take.
After replacing the HDD (guides found via ifixit.com or even that manual that came with your Mac) and having made sure, you properly backed up via Time Machine, insert the Snow Leopard DVD into the Superdrive, hold down "C" after the startup sound.
Now your Mac starts from the SL DVD.
When you are asked what language you wanna take, select the one you like.
After that you can go into the Menu Bar, select Utilities > Disk Utility and there select your new HDD.
There you can chose to erase the HDD (Erase tab) and format it with Mac OS X Extended.
It will take some time (mere minutes), after that you quit Disk Utility and continue with the installation.
At one point you will be asked if you want to import/migrate data from another Mac or Time Machine backup.
Choose Time Machine and then you can also select what you want to have restored.
There is also another and easier way to do the whole replacing procedure.
Buy an external 2.5" HDD USB enclosure, put in the new HDD, download CarbonCopyCloner, clone your internal HDD to your external HDD.
After that is finished, replace the two HDDs, and then you can just boot up from the new HDD without having to reinstall anything.
Now you can also use the old HDD as external storage in the USB enclosure.