Tile map structure

I have the A* pathfinding working (lightgreen, green destination)
The red circles are units, 1 smaller than a tile, 1 bigger.
Now i wonder what's the best way to let the units move the path ( lightgreen ) without colliding with a wall or later an other obstacle (might be bigger or smaller then a tile.) Whats the best way to do this and smoothen the path (like the red line.)?

Also how are tilemaps normally structured?

Is it like (pseudo)
this.map.move(unit,[x,y]) or rather this.unitmanager[selectedUnit].move([x,y]);

Someone has some good tuts or sample source.

Thanks in advance.