Q:

Why are some UI elements cut off along the edges of my TV?

I just recently got Skyrim. I never knew about the bar at the top saying which way to go for a quest up until recently when I was watching other friends play it and some youtube videos. 
My TV is not HD, and is about 32 inches, and it doesn't show that stuff. Even watching TV I notice big lettering not showing on the sides. My remote doesn't work and I don't believe it is compatible with a universal remote due to it having both a DVD player and a VHS player built in. 
How can I get the whole picture to show up on my old TV?

A:

The issue you're experiencing is called overscan: where parts of the image that your television displays appears to be "cut off" on each side, or bleed outside of the visible area of your TV screen. The behavior is extremely common on CRT televisions, but some newer flat-panel TVs/HDTVs perform overscan by default as well, for a few different reasons. However, many modern television models include a menu option somewhere allow you to reduce or eliminate the overscan effect, though it's not uncommon for that setting to be buried fairly deep if it does exist.
One bit of good news is that even if your television doesn't allow you to adjust the overscan, many games include a "Screen Adjustment" or similarly-titled option in their own settings menus. This will allow you to tell the game what the visible area of your TV screen actually is, so that it will make sure to draw all text and UI elements within the screen area that you can actually see. Not all games include this sort of feature, though.
You can read more about overscan and why it exists here.

