I have to synchronize the movement of multiple players over the Internet, and I'm trying to figure out the safest way to do that.

The game is tile based, you can only move in 4 directions, and every move moves the sprite 32px (over time of course). Now, if I would simply send this move action to the server, which would broadcast it to all players, while the walk key is kept being pressed down, to keep walking, I have to take this next command, send it to the server, and to all clients, in time, or the movement won't be smooth anymore. I saw this in other games, and it can get ugly pretty quick, even without lag. So I'm wondering if this is even a viable option. This seems like a very good method for single player though, since it's easy, straight forward (, just take the next movement action in time and add it to a list), and you can easily add mouse movement (clicking on some tile), to add a path to a queue, that's walked along.

The other thing that came to my mind was sending the information that someone started moving in some direction, and again once he stopped or changed the direction, together with the position, so that the sprite will appear at the correct position, or rather so that the position can be fixed if it's wrong. This should (hopefully) only make problems if someone really is lagging, in which case it's to be expected. For this to work out I'd need some kind of queue though, where incoming direction changes and stuff are saved, so the sprite knows where to go, after the current movement to the next tile is finished. This could actually work, but kinda sounds overcomplicated. Although it might be the only way to do this, without risk of stuttering. If a stop or direction change is received on the client side it's saved in a queue and the char keeps moving to the specified coordinates, before stopping or changing direction. If the new command comes in too late there'll be stuttering as well of course...

I'm having a hard time deciding for a method, and I couldn't really find any examples for this yet. My main problem is keeping the tile movement smooth, which is why other topics regarding synchronization of pixel based movement aren't helping too much.

What is the "standard" way to do this?