A teep literary means a foot jab. It is a straight foot-thrust and it should be done in a single fluid motion: raise your leg, thrust it straight out and then pull it back in and place it down.
A teep is the most useful for targeting hips, abs and solar plexus. In some ocassion even a face. Targeting the other fighters's face with a teep is one of the bold ways of showing a domination in the ring.
A push kick also serves as an intercepting kick against opponent's kicks and punches. It also helps to keep him on the distance. Just don't let your kick to get caught and counter-attacked with a leg sweep.
You can also use a front kick to set up an attack. It goes well with push kick+round kick or even a push kick+elbow combination like:
left push kick + right round kick
right push kick [close the gap] + left elbow. Raise a right elbow immediately after strike to protect your face from a counter-strike.
Round kick is a semi-circular, 45 degree kick used to target all parts of the opponent's body.
A low kick targets thighs and knee joints, mid kick aims for the rib cage and a head kick which targets opponent's neck.
To perform a round kick, bend a leg a little and swing it to the designated area of your opponent's body. Move forward to kick and keep your guard up. It is useful to wear your opponent down and limit his movement by targeting his legs.
Round kick, thanks to its power, is the most common kick used in K1/Glory and MMA competitions. A well delivered roundhouse kick has the same impact on a human body as being struck by a baseball bat.