Using Just a Portion of Existing Photo

EDIT: Sorry, could one of the mods please move this to the "Photoshop Forum". I didn't mean to post it in Tutorials.

This is my first post on Team Photoshop so I'm going to give you a little back-story. Forgive me if it seems like I'm rambling.

I'm a Computer Programmer by day and an aspiring web developer by night. I've been fiddling around in Photoshop for a few years but I'm really still a beginner when it comes to knowing what I'm doing. I can do very simple image manipulations but that's about it.

So, I've been recruited by a friend of mine to design a website for a charity that is coming into my city. This charity is quite large but they leave the local websites up to the individual cities (some of the sites are kind of weak). I told them I would design the site for our area so I'm starting this weekend.

The first thing I'd like to do is manipulate a photo, but I'm not sure how.
I don't want to post the actual file or tell you who I'm working for because I'm a man that enjoys privacy...but I will submit an attachment as an example. Let's say this charity's logo is the "TIVO" logo (attached). For the design purposes of this site, let's say I want to pull the letter "V" out of the TIVO logo. The way I would do it, with my simplistic knowledge of PS would be to first "crop" the V and get rid of everything else. Then, to tidy it up, I'd zoom in really tight on the "V" and go around by hand touching up the area around the V to match the background color on my site.

I'm sure there is a way that this can be done with much more precision and speed. Am I right?

If the actual file you are working with is similar to the tivo logo, just use the magic wand tool and click on the V. It will select the whole thing in one click. Then you can copy/paste what have you. Another option is to go to Select > Color Range then use the eyedropper tool to select a certain color range. You can adjust the sensitivity of both of those tools to get the results you need.

If it is not a solid color, you could try using the Pen tool to create a path that selects the letter or object then turn it into a selection. Or you could use the lasso tool and do it by hand. There are a million different ways to accomplish something in photoshop, just depends on your experience and what your project requires really.