There are 13 spades in the deck because there are 4 suits and 52 cards and 52/4=13. If you randomly picked one card from the deck, the odds that it is a spade would be 13/52=1/4, which makes sense because there is an equal chance of drawing any of the 4 suits.
Now once you draw your first card, there are only 12 spades left in the deck and only 51 cards total. So for your second card the odds of it being a spade is 12/51.
So the total probability of both of them being spades (without replacement) is
I imagine you keep getting because you are doing the problem with replacement, meaning you first draw a card, then look at it, then put it back in the deck and draw again, in which case the answer would be as the calculation would be