There are many methods to protect your pieces when they come under attack from your opponent. Not all of these methods will work in an actual game, but all should be considered depending on the situation that you find yourself in.
The first method is to move the piece to a safe square. This would be a square where your opponent cannot attack the piece or where it is guarded by another piece of yours.
A second method to protect an attacked piece is to capture the attacking piece. This may be one of the best methods because not only do you eliminate the threat from your opponent, but you also gain material and tempo in the process. Your opponent will have gone from an offensive front to a defensive posture in this one move.
The third method is block the attack. This does not work with all pieces such as knights. If you opponent is attacking with a queen, rook, or bishop this method will work. This is where you simply move another piece in the path of the attacker so that your opponent cannot capture your primary piece.
The fourth method is to simply guard your piece that the opponent is attacking. Moving another piece does this, so that if your opponent does attack, you will be able to capture the opponents attacking piece the very next move.
The final way to protect an attacked piece is to counterattack. Pinning or skewering your opponent can do this. For example, if your opponent threatens to take your rook, but you are able to threaten to capture your opponent's queen, then your opponent is likely to surrender the attack and to defensively move his or her queen.