Generally the jump foot is simply the foot you feel most comfortable with. When I first started coaching I was extremely surprised at how many athletes would ask me "which foot should I use?" Below you will find general suggestions that I tell my athletes every year in regards to both long and triple.
It's all about comfort!
If an athlete is going to be successful he/she must first and foremost be comfortable. There should be no discomfort or sense of uneasiness in any aspects of their jump(s). By letting them know that you will help them choose, but that the choice is ultimately up to them helps them to take ownership of that choice.
One of the best ways to find the "right" jump foot is to have athletes simply do short approach jumps. Instruct them to stand roughly 10 feet away from the pit, do a slow jogging approach, and jump. Most likely he/she will end up jumping off a certain leg (which 9/10 times ends up being their jump leg). Here's a video that I found on YouTube of this in action:
The above approach generally helps an athlete to figure out any questions they might have regarding their jump foot. If not, there is another drill that I use on a yearly basis that I feel has some extremely strong merit.
Watch the video to learn more.
What about the triple jump?
The triple jump is pretty tricky. If you were to research which foot to use in your first takeoff you find a large number of differing opinions. Again, this should mostly be about the comfort of the athlete. But, there are also some other considerations here that need to be part of the equation.
Consideration #1 - The amount of "pounding" the athlete's legs are taking. If an athlete is a long jumper AND a triple jumper they may want to use different takeoff legs/feet to preserve the health of their legs to the best of their ability. Personally, this is NOT the route I have my athletes follow, but it definitely is something to keep in mind. I would only use this one in severe cases (of leg discomfort and/or injury).
Consideration # 2 - Use the same leg you do long jump with because your body has proven that is leg is is most comfortable with. You spend two thirds of the triple jump taking off from one leg - why not use the one that is most coordinated/strong? Like I mentioned in the first consideration though, you must keep track of the "pounding" that leg takes, and never jump the athlete in both jumps at practice and/or meets (unless you have planned a very low impact workout).
Consideration # 3 - Coaching observations. Coaches need to understand what to look for when training their athletes. If a coach is working on bounding and realizes that a jumper bounds better on a certain leg that is important! The coach might suggest that the athlete make sure to use that leg/foot while performing both the hop and step phases. Coaches, it's your job to be observant in everything your athlete does. Pay close attention and make suggestions when necessary.
Consideration # 4 - Overall coordination, hip flexibility, and strength of the athlete. If there is a lack of strength, coordination, and/or flexibility in a certain leg I would suggest using that leg to perform the jump phase. Strength, flexibility, and coordination are SO important in the hop and step phases that you will want to use the leg that encompasses most of those focuses. I am a firm believer that the step phase is what separates the great jumpers from the rest. Without performing this phase properly athletes can only hope to be average. For this reason, finding the proper leg is extremely crucial to the overall jump.