How does one determine the proper foot to use when taking a shot on goal in football? For this question assume the player is equally skilled with both the left and right foot. I'm assuming position on the field is a contributing factor.
There are a number of factors in determining which foot to shoot with in football, including:
Position of the Ball
Due to the mechanics of dribbling (and naturally, passing), the ball is rarely directly under the player's centre of mass (and it is extremely difficult to strike the ball effectively from here.) The ball will often be on the left or right side of central to the player, and should be struck with that foot accordingly.
If a ball is being crossed to the striker, proper technique is to place your body in line with the path of the ball and strike across your body against the movement of the ball (rather than across the movement of the ball whilst facing the goal, which is a lot more difficult to control.) This will determine the foot you strike with for you; if the cross is coming from the left, natural body movement will dictate that you strike with your left foot.
Position of the Player Relative to the Goal
A player should strike the ball with the foot that affords the largest target area of the goal to aim at. If the player is on the left side of goal, this is the right foot and vice-versa. This is due to the action of striking the ball, which opens the body in the direction of the foot being used. If you strike the ball with your left foot on the left side of goal you are turning your body away from goal, which makes it more difficult to shoot towards the far post.
Position and Movement of the Goalkeeper (and/or Defensive Players)
A striker should always attempt to place the ball in a manner that makes it as difficult as possible for the defending team to stop the shot. If the goalkeeper is moving or shifting their body weight to your right, shooting with your right will allow you more control and power in striking it to your left. The mechanics of movement in defence will also often allow a striker to place a shot between a defender's legs with one foot but not the other.
Desired Movement of the Ball
If you want a shot to curl from right to left, it is easier to do so using the instep of your right foot. Whilst possible to do so with your left foot, it is mechanically harder to impart as much revolution on the ball whilst maintaining control. Similarly, it is easier to strike a placed curled shot from left to right using your left foot.
Even in the hypothetically perfectly skilled two-footed player, a striker is going to have a preferred foot. If there is no mechanical reason for choosing which foot to strike with, the player will default to the most natural foot.
Of course, there are plenty of one-footed players who are quite capable of striking effectively against the preferred mechanical option. Sometimes taking the less conventional option will be more effective in catching the defence off-guard. Proper striking technique is more important that choice of foot.
[Source: 25 years of playing football, Junior coaching licenses.]