I think it's possible if you have anything better than windows movie maker. lol. I use mostly Adobe After Effects to edit my videos, but that's kind of expensive program. Especially if you only need some texts etc. lol.
But what are you using to edit your videos? :o

Can you be more specific?

Well, It kinda depends on what kind of computer you have. With a apple product (lets hope now, many would say) You would use final cut pro, pretty awesome and easy yo use. This is what I was taught to use in my video editing class. Basically, you drag the video down into the program, and you add stuff. Its pretty simple because, well I think there is a add text box option. If you don't have an apple product, well there are a few more out there, but you need something, like the person before me said, better then movie maker. Basically what they had said with more information.

In the end though, you kinda need to post your software to get more detailed and specific answers. That way people could help you more D: Wish I could have been more help, as I don't really think I helped any.

I think PewDiePie is using Sony Vegas Pro 10/11/12 for editing his videos.

He uses Adobe Premier

If you're on PC, and you want to do the same thing , well. He uses premiere which is a top-notch video editing software but it requires some skill. (well all of them does).
For only that, Sony Vegas would be easier thanks to it's friendly interface, but it's not as reliable as the premiere. And when you'll edit, don't think there's a plug-in which helps with putting the words together. You have to listen to the video , and write every sentence as it can be heard in the video. It's an easy process but a long one. It requires patience.

I made this when I started using Adobe After Effects: youtube.com/watch?v=yTmFEeeUYJY

Camera movements are bad because I made it over a year ago, when I was just starting to learn after effects. But yeah I made it listening to the lyrics and writing everything seperately. And then just putting them on the right places.