Compound Butter sounds like something difficult . Actually it is very easy. A Compound Butter is simply adding other flavors to butter. The idea is to add some intense flavor to the butter so that a small amount will add an accent of that flavor to anything you put it on. Garlic butter is a compound butter.
Here are some simply but tasty ways to do that.
1. For steaks add roasted garlic and some blue cheese crumbles. Or you can saute some shallots in butter until they are tender, deglaze with vermouth and add that to some more butter. Either on of these will add a certain flavor to any meats.
2. For seafood - add some dill or tarragon. You can also add some shallots or any herb that you like.
3. Vegetables - I like dill or oregano with a lot vegetables. Especially if you grill them, Add the compound butter just as you serve the veggies.
Try some Lemon in the butter too - it really adds a zing. Or peppers or - the list is endless!
Experiment and see what you like.