Training is simple and yet complicated, but the following principles apply regardless of whether a person is training for a marathon or a bodybuilding contest.
Principle of Overload
This principle is derived from Hans Selye's General Adaptation Syndrome (GAS) where a greater than normal stress is needed for training adaptations to take place. You have to do a little more than your body is accustomed to doing in order to create a stimulus for adaptation. For instance if you run all your runs at 9 min/mile pace then you cannot expect to run very far at a faster pace.
Overload can be induced by increasing training volume or training intensity. Volume can be increased through more sessions per week or more time spent in each session. Let's say you are running 4 days per week now; you can increase the volume by adding a 5th day. If adding a day is not possible, then you could add time (or miles) to each run. Intensity can be increased by running faster or maybe adding hills.
Principle of Progression
Progression is related to overload in that you must gradually and systematically increase the stimulus over time to get improvements. The pace of this increase is critical to reduce the risk of injury. Too much too soon is a common cause of overuse injuries especially in new runners.
Principle of Specificity
There are a couple of aspects to this principle. One is that training moves from general to specific. For instance a soccer player during the transition (off-season) might do general conditioning for overall fitness and then as the season approaches will have training that looks more like what a soccer match would demand.
Another aspect is that to be good at a sport you need to practice or train in that sport. So to be a good runner you need to run. Riding a bike will have minimal impact on improving running performance. This not to say that non-running training should be avoided just that it needs to be placed in perspective and also for performance needs to be transferable to running.
Principle of Individual Differences
As the name suggests, training needs to be adapted to the individual. This is a reason that "canned" training plans as might come from a website or book are problematic. For a good number of people they will help achieve a goal, but we all respond differently to the same training stimulus. Two people on the same marathon training program might have very different results.
By the same token, you cannot expect a 20-something runner and a 50-something runner to be able to follow the same training plan. How is this for a twist: What if the 50 year old runner has been running for 35 years and the 20 year old just took up running? The older runner may well be able to handle a heavier training load.
Principle of Reversibility
This could also be called the "use it or lose it" principle. If you stop training you will see a reduce in performance. The rate of loss varies depending on the trait. Typically the faster a trait adapts the faster it is lost. Some traits are structural so they reverse slower. In endurance training, an quick adaptation is plasma volume expansion or increasing the amount of water in the blood. Well, if you stop running your plasma volume will return to normal in about seven days. Another adaptation is creating new capillaries (angiogenesis) around slow twitch muscle fibers. If you stop training, it takes a lot longer for those to disappear.
Principle of Warm Up and Cool Down
Warming up should precede exercise especially if the intensity is going to be high. Admittedly, I am a slacker about warming up before easy workouts although I am adding Jay Johnson's lunge matrix and leg swings to my clients' warm ups. The purpose of the warm is to increase body temperature, heart rate and ventilation rate while also dumping a little acid into the system. All of these things help improve performance.
Cooling down is kind of interesting. I recommend cooling down, but some researchers are questioning the need. I would say that if the session were intense, then cool down to buffer the acidity in the body primarily through maintaining an elevated ventilation rate. Personally I know I feel more stiffness when I do not cool down even it is walking a bit after a long run.
Stretching needs a mention here. I am not a fan of stretching as part of the warm up except for specific instances. However, stretching after the workout as part of the cool down seems like a good idea.
Those of the principles of training regardless of the physical activity. I hope that helps with the terms if you come across them.