Groundstrokes are the most fundamental shots in the game. There are many different ways of hitting the forehand and backhand. As you play, you will realize your strengths and tendencies of your swing. Your swing is unique to you; "different strokes for different folks" is the motto. So, don't worry if your shots don't look like the pros, but there is one fundamental technique when it comes to hitting a topspin groundstroke. You need to swing forward, low to high, and brush up on the ball. For an underspin shot, you need to swing forward, high to low, and brush down on the ball. Sidespin is the idea of brushing the ball left to right or vice versa. Also, it is important to know that the trajectory of the ball is determined by the geometry of your racket strings. The ball will generally go where the racket strings are pointing.
If you are right-handed, your forehand is on your right side. There are two ways I like to hold the forehand grip. One, using your left hand, rotate the racket so that edge of the racket is pointing down to the floor. Then, use your right hand to give your racket handle a hand shake. This grip is the Eastern forehand grip. Two, place the racket on the floor and pick it with your right hand. It should feel as if you are holding a frying pan. This grip is the Semi-Western grip.
On the left, there is a gif of me doing a forehand. An analogy to a forehand technique is like an underhand lob of a tennis ball. You will notice that your arm is relaxed, and it accelerates through the swing. A racket and a ball both are not heavy, so it is not nessecary to muscle your swing. Actually, tensing up your arm when swing is detrimental to the groundstroke. Like a good lob from a underhand throw, you would use mostly your bent legs and rotated shoulders. In tennis, your legs and shoulders should always be the source of power and racket speed.
It is possible to hit a backhand with either one hand or two hand. For the one hand backhand grip, hold your racket two feet in front of you with you left hand. The racket edge should be pointing up and down. Then, place your right palm on top of the handle. This is your Western backhand grip. For the two hand backhand, your right hand should be on the bottom of the racket handle, while your left hand should be above your right hand. To begin holding a two hand backhand, you should shape you right hand like a "U". Then, the right hand slips into the narrow side of the handle, and it feel like holding a hammer. This is your "Continental" grip. With your left hand, you should hand shake the handle above your right hand holding an "Eastern" grip.
The backhand is also very similar to doing a lobing a ball just like your forehand. Imagine with your one hand backhand that you throwing a underhand lob with the back of your hand leading the throw. For the two hand backhand, it is like underhand lob of a light ball with two hands. Both the one hand and two hand backhand uses the shoulders and legs as the main source of power and racket speed.
The slice is usually held with a "Continental" grip or the hammer grip, but, like all groundstrokes, you can use any grip you can think of. The swing of a slice is like waving a flag. A flag has some drag in the swing, and you should still make sure you accelerate forward through the ball. It very important that you swing forward through the ball, or else the ball hit the floor or lob really high. In order to swing forward through the ball, the racket begins high, swings low as the strings contact the ball, and immediately afterwards, swing up to push the ball forward. This is a difficult shot to hit, but with practice you will hit a perfect slice.