It isn't the case that someone is always willing to buy at the same time someone wants to sell. What happens is if you want to sell your stock you can either find someone willing to buy it or you put out a sell order that basically is a notice saying "I'm willing to sell Y stocks for X amount of dollars." In which case you sit around and wait till someone is willing to fulfill that order.

On the flip side someone wanting to buy one can either grab one for those immediately willing to be sold or put in a buy order for a certain price.

So when you sell you're either fulfilling one of those buy orders or your putting in a sell order yourself and waiting for someone to buy it.