The placement of your foot on the pedal when riding bicycle or unicycle is an important factor in affecting how much you enjoy riding. If you position your foot improperly, your ride will be uncomfortable. Using the proper foot placement increases efficiency and reduces the possibility of injury. The standard foot position is efficient and—unless you are doing a specialized type of riding or have unusual anatomical reasons—is the most comfortable.
NB: I have no special training, this is article is based on my own experience, observing others, reading about cycling efficiency, and discussions with other cyclists. If you get hurt, it's your own fault
Use this foot on pedal position unless you have a really good reason to use one of the other positions. Notice that the ball of the foot is directly over the pedal spindle. Your foot may be slightly tilted toe down during part of the pedaling motion, but not significantly, and it will never be heel down. Unless you have a specific reason not to use the standard foot position, it is the best way to ride.
The Big Drop
For riders doing big drops, it is often a good idea to temporarily shift the foot forward. This is inefficient for pedaling, and risks damaging the arch of your foot, but some riders believe that when used for big drops while wearing stiff shoes it can be worthwhile to prevent Achilles tendon injuries. Some level of shift can also be used for other problems, for example it can be used for one foot by riders whose feet are significantly differently sized. Remember, feet are meant to be supported at the heel and ball, not on the arch, so you must weigh the risks of Achilles tendon damage and the risk of foot damage (eg plantar fasciitis). I only use this position when I nearly miss a unicycle mount, and recommend that you avoid it.
Some unicyclists prefer this for off-road riding. It is common among those with excessively tight Achilles tendons. It can be a useful compromise between the standard and the Big Drop foot positions, but use the standard when possible. It can also be useful when unicycling on rough terrain to minimize the problem of getting stuck at the bottom of a pedal stroke.
The exaggerated tilt-shift
The slightly tilted, slightly shifted forward position can help when learning to unicycle. If you are having a hard time pedaling smoothly through the bottom of the stroke, temporarily using this foot position can help you learn to make it past the bottom-out point. If you use this foot placement, you should try to move to the tilt-shift position as soon as you are able. This foot position is really only good on a smooth surface when first learning to unicycle.
This foot position is commonly seen used on department store and semi-recumbent bikes. This is usually seen on bikes with the seat way too low. It is so inefficient and awkward it makes cyclists wince to see someone else use it. Fortunately, you usually have advanced warning that a rider using this position nearby because their bicycle usually emits loud metal-on-metal screeching noises. If you pedal like this, please switch to the standard position immediately. Your knees will thank you.
For some riders—famously Lance Armstrong—hard efforts are done with the toes aimed significantly down (heel up). This is only used when pedaling at extremely high cadence; during normal efforts the standard position is used.