On floors, most of the edges of tiles will be covered with a skirting board or door threshold strip, but on worktops you will need to cover the edge of the tiles with a piece of hardwood strip or a purpose-made tile edging. This could be plastic or special round-edged tiles.
It is best to place the strips in line first and then tile away from them towards the back edge. If the tiles meet a wall, then the wall tiles should be placed over the cut edges of the worktop tiles. Use a silicone sealant along the back and then tile over it.