AA: (Or any pocket pair)

4 ways to draw the first card, 3 ways to draw the second card.
Since we are calculating the probability of being drawn two aces, we multiply the chance of being drawn the first ace by the chance of being drawn the second. So we have:

4/52 * 3/51 (which reduces to) = 1/13 * 1/17 = 1/221

Therefore your chance of being dealt AA is 1/221. This is actually the same result for being dealt any specific pocket pair, because the probability of being dealt each card is calculated the same way. So if you wanted to find the probability of being dealt say, pocket 7's, it's the same method.

AKs: (Ace Dealt First) -see tyrn's correction for combinations, this example was created using permutations, which assumes order matter, when in practice it does not.
This is slightly different, but the main thing is to keep in mind the theory - the theory does not change. Simply count how many cards are left that make the hand you're trying to find the probability for. Ask yourself how many cards are left in the deck that make my hand after I am dealt my first card?

There's 4 ways to choose an Ace out of the deck, as we know. However, there's only one way to choose the King for your hand to be suited, therefore:

4/52 * 1/51 = 1/13 * 1/51 = 1/663.

So as you can see, when you want to find the probability of being dealt AK suited (when being dealt an Ace first), you must remember that there is only one way to choose the second card to match your suit.

Now you know the theory, you should be able to figure out any other cases.

(8 ways to choose first card for AKs for combinations, 1 way to choose second)