Upgrade failed to download from Mavericks to Yosemite Apple newbie here. I tried to update OSX from Mavericks to Yosemite. The downloading failed. It showed me a message saying "an error occurred". So what I did is to search on google what were the recommendation. I followed this video tutorial to reset the download again here.

After doing that the message was gone although the button now turns to just "Download". 



It prompt me to restart my computer to install. But I was worried because I know that the download failed. Any suggestion on what to do? Is there any way to re-download the update just to make sure I have all the files.
That's good that you're approaching things cautiously! However, you do not need to worry about this; Apple has built in multiple levels of protection to prevent you from messing up your computer. 

There are two larger protections:


The App store automatically makes sure that the file you downloaded is what you were supposed to download and fixes anything it sees wrong.
When installing, the Yosemite installer double checks that the installation files are all in order and stops the installation if not.


Therefore, you should be okay to just go for it and upgrade.