Frying

I'm a little bit new to frying, but I love donuts. A couple weeks ago, I made Alton Brown's donut recipe, and it turned out excellent. But the quart and a half of oil is still hanging out in my dutch oven. I have heard conflicting reports about reusing oil. Could y'all set me straight? When and how is it appropriate to reuse vegetable oil? How do I dispose of it? Can I compost it? The last time I used donuts, the recipe said to use shortening to fry, but I didn't like the taste, why would I use shortening?

-Loafer