I used to coach high school wrestling, and wrestled for the greater part of a decade myself. Especially when we look at training high school athletes for performance, wrestlers may be one of the most diverse athlete populations you may encounter. Not necessarily due to demographics, though it is one of the oldest and most traditional sports in the world, but due to the demands at which the sport presents. Wrestling, as a whole, requires some of the broadest range of abilities an athlete can have.
I'll first start by saying, wrestlers have very similar demands for high school athletes as more common sports such as baseball, football, and basketball. But they're unique because they also need similar qualities as soccer players, track athletes, cross-country runners, and gymnasts. What does this mean?
A high school wrestling match which goes the distance is at least 6 minutes long, but can go as long as 10 minutes long if they go into overtime. This 10 minutes can be absolutely grueling, as those who have gone into the final minutes of an overtime can tell you, it will take everything in you to win. Within these 6-10 minutes (though some matches can last as few as 3-4seconds...), there will be an expression of qualities from a speed, strength and power, and conditioning standpoint which need to be considered for training. And they need to do it within the bounds of maintaining weight to fit into a weight class.
Speed Considerations
Regardless of the weight class, wrestlers need to have a solid baseline of accelerative speed. A wrestling mat is a minimum of 28ft in diameter, though most are ~30ft. Wrestlers need to be able to express their speed linearly and laterally within these confines. To train this, most speed work should be targeted in the 5-10yd range and should vary in starting position and direction. Additionally, as part of this accelerative process, wrestlers will unconsciously use "plyo-steps" (the brief loading of tendon structures) prior to making fast shots. Incorporating lower level plyometrics such as pogos, low hurdle hops, and line hops can be very beneficial.
Strength and Power Considerations
Like all athletes, wrestlers need strength and power. Strength is crucial from a physical and psychological perspective, as having (or feeling like you have) a superior level of strength can play a difference in how matches flow or which tactics get used. However, this strength and power has to be expressed within the confines of making a weight class 1-2 hours prior to competing. So being able to have a relative power output and relative strength is also key. There's a lot of ways to skin the cat in this regard, which can be covered in other blogs, but there's one other consideration for strength which then needs to be factored in: odd/unstable positions. Wrestlers may find themselves in some really odd positions, or positions of high joint instability. This requires they train the full spectrum of length-tension relationships and train in odd movement patterns. This will need to be be considered across training cycles.
Conditioning
Conditioning considerations can get a little funky with wrestlers depending on strengths and weaknesses, or wrestling style (both rules or tactical style). For Folkstyle wrestling, the primary style of Pre-Collegiate and Collegiate rules wrestling, you can stereotype wrestling styles as traditional or funk. Traditional wrestlers are brawlers. They hang heavy on the head, use force to move opponents, and display power in short bouts. These wrestlers (or programs with this style of wrestling) tend to need to build bigger aerobic bases. You need a high mitochondrial density to be able to carry around the muscle mass and not lose steam in the later minutes of a match.
For wrestlers who use a bit more of a funk style, which uses space, length, and fast flurries of movement to create gaps and holes in their opponents defenses to score. These wrestlers tend to be your lighter weights, or lankier athletes who use their weakness (often times being physically weaker) to their advantage. These funk style wrestlers need a bit more anaerobic conditioning, in order to be able to withstand the beating they may take at the hands of a traditional style wrestler. The more a "funky wrestler" can hang on anaerobically, the more opportunities they have to win in later minutes of matches when they can rely on what is usually a higher aerobic capacity. For each of these styles of wrestling, conditioning strengths and weaknesses will need to be addressed, and can be identified by talking more with sport coaches and by reviewing film.
Now, there's a lot more depth to each of these. When and how you train each of these components will also depend on any off-season plans and styles of the sport they compete in during the year as Freestyle and Greco-Roman wrestling have slightly different demands. It will also have to be based on any other sports they may participate in throughout the year to build some of their general athleticism. Regardless, these things need to be considered when looking at training High School level wrestlers.