The first step is to clone your MacOS disk to the new, larger disk.
Back everything up. This goes without saying, but you should have all of your files backed up to a third disk, which you will put aside and not touch during this process. I use
Time Machine for this backup.
Plug the new disk into your Mac. If you have a Mac Pro, you'll likely be able to connect it to one of the internal bays. If not, you'll have to get a USB enclosure, put the disk in that, and connect it up.
Open Disk Utility, and locate the new drive. Partition it with a single partition, using MacOS Extended (Journaled). NOTE: Even if you're also migrating a Boot Camp partition, you want to partition with a single MacOS partition now. Later, you'll use the Boot Camp tools to carve off part of this new partition for Windows, and then restore your existing Boot Camp partition using WinClone.
Reboot your machine. Technically this probably isn't necessary, but I like to have an absolute minimum of other applications running when I'm cloning my disk. You should not use your machine during the cloning process.
Open Carbon Copy Cloner, and perform a full disk clone (the 'Backup everything' option) from your old disk to your new disk. This will take several hours to copy all the data. I recommend you click 'Delete items that don't exist on the source' so you get an exact clone.
If you also want to migrate your Windows Boot Camp partition, create an image of that partition once Carbon Copy Cloner has finished. Open WinClone, click on the 'Image' tab, select the Boot Camp partition, and hit 'Imageā¦'. You should be sure to save the image on your new disk, because you're about to get rid of your old one. Again, make sure you start this step AFTER Carbon Copy Cloner is completely done; you should only have one cloning program running at once.
Turn off your machine and swap the new disk for the old disk. Doing the physical swap usually isn't too hard, but the details depend on what Mac you have. Once again,
iFixIt has some great guides.
That's it! Once the disk is swapped and the old disk is removed, boot up onto your fresh disk!