I like to use freshly grated citrus peel and also freshly squeezed citrus juice because it makes a huge difference in the taste of recipes.   Here are some hints on using lemons, limes, oranges, and even grapefruit in recipes.

To get more juice, soften a lemon, lime, orange, or grapefruit for 10 seconds in the microwave. 

Since I always have hot soapy water in my sink when I'm cooking, if I'm planning to juice lemons, limes, oranges, or grapefruit, I put them in the hot soapy water.  This not only cleans any dirt or germs off the skin (I rinse the soap off of course), but it softens them so I'll get the maximum amount of juice.  I dry them thoroughly after rinsing, then take the zest off before cutting the fruit in half and juicing.

Lemon, Lime, Orange, and Grapefruit Zest:

If you've ever purchased a jar of dried citrus zest, you already know that it is very different from fresh zest.  Personally, I don't think it is worth the purchase; it is almost worse than having no zest at all.  Whenever I need to juice a lemon, lime, orange, or grapefruit, I grate the zest off first either to use in a recipe, or to keep in my freezer until needed.  I keep fresh zest in the freezer in labeled Ziploc bags;

If you need large pieces of zest, you can use a potato peeler.  Be careful not to get any of the white bitter pith.  If there is some pith on the pieces of peel, you can scrape it off with a sharp knife.  These wide strips can be put in ice water and curled for garnishes or used to flavor boiled syrups such as the one I use for Baklava.  You can also boil these wide strips in sugar syrup, then dip them in sugar for homemade candied peel.
A zester, which is available in most department or cooking stores, makes long thin strips of zest.  These strips are good to use for garnishes.  They can also be candied.
A microplane, which is my favorite tool for zest, allows for extremely fine zest very quickly.  Whenever I need fresh lemon, lime, orange, or grapefruit juice, I grate the zest off prior to juicing.

Juicing:

I purchased an inexpensive (under $20) citrus juicer which makes the juicing very easy.  If you make a lot of recipes that call for fresh citrus juice, it might be a wise investment for you.  The citrus juicer has a screen that keeps most of the seeds out of the juice so it doesn't have to be strained. I also have an all-purpose juicer, but I find that it isn't suitable for citrus because it puts too much of the white pith into the juice which makes it bitter.
If you don't do a lot of citrus juicing, a hand juicer will work just fine.
A reamer is also a handy tool when you just need to squeeze the juice into a recipe.

Disposal of Citrus Peels:

I always put my citrus peels in the garbage disposal since they freshen the disposal and make the kitchen smell really good.