Suppose a player loses his footwear accidentally while playing and then scores a goal without wearing his footwear. Will it be considered a legal goal?
There is a law regarding such situation:
A player whose footwear or shinguard is lost accidentally must replace it as soon as possible and no later than when the ball next goes out of play; if before doing so the player plays the ball and/or scores a goal, the goal is awarded.
NB: hims056's answer is correct according to the law but I will add the following supporting information.
A lot is said in football about the referee's "interpretation" of the rules in a match. In the interpretation of this law, we should look closely at the term "immediately".
You will very rarely see a referee award a free kick against a player who passes or shoots with an un-booted foot. The player is at a disadvantage by being missing a boot so the generally-seen interpretation is that the player has had his shoe removed by accident.
With regards to the immediacy of the event, you're not likely to see a player running around for 15 minutes without a boot so pretty much any time from the loss of the boot up to the next time there is a break in the play could be deemed (interpreted) as immediate.
To sum up the interpretation as simply as possible; if the player has lost a boot and he hasn't had chance to replace it, then he will not have a foul awarded against him.
Earlier this year, Alessandro Matri scored for Juventus wearing no boot on his right foot.