I just recently bought the maxed out edition of the Razer Blade Stealth and noticed that the storage space got cramped pretty fast. I have my eye on an SSD I want to buy so I can switch them out, but I have no idea what to do once I have my new SSD.
Depending on which drive you purchase you will need a USB adapter to your drive form factor. I believe the Razer blade stealth has an M.2 so you will need an adapter accordingly. Some of them come with an image copy utility, but if your drive comes with one I would use it. Hook the new drive to the adapter, copy the entire image over and then put the new drive in place of the old one. Samsung and Intel both came with a copy utility, not sure on other brands.