Sure, on most every Toshiba laptop I've ever worked on, the HDD is very easy to remove. You just need a Philips #1 screwdriver. Usually there's a removable door on the underside of the laptop. I've never worked on your specific model, so I can't tell you exactly.
But any 2.5" SATA HDD should work. There is a small possibility that yours is a PATA/IDE HDD, so it may not be a bad idea to remove the existing drive and take it to a local electronics/computer store and make sure that the "business" end looks the same. After that, you should be good to go.
If you're planning to buy online, I generally don't look any farther than NewEgg. They aren't always the cheapest, but they are a very reputable company and they don't screw around. If, for some reason, NewEgg doesn't have the part, I might try Amazon. Don't think I've ever run into a situation where one of those two doesn't have the part I'm looking for.
My computer is out of warranty. I can't afford and WON'T pay $200-$500 to get a 2 year old computer fixed. I purchased recovery discs from the company (Toshiba) and they won't work. The error codes I'm receiving indicate - according to customer support - that there is something wrong with the hard drive. After trying the recovery discs I got a message that says
SMART Failure Predicted on Hard Disk 4 - read on the internet that that is definitely a hard drive failure/issue.
Can I replace the hard drive myself? What part sellers do you guys recommend? Any tips I should know?
Model: Toshiba Satellite A355D-S6922