Special "mortar chisels" fit perfectly between the bricks, allowing you to get rid of loose or poor mortar without disturbing the brick. Whenever you are going to add mortar to existing brickwork, you must make sure that the layer of new mortar will go as deep as it is wide. That is because it adheres primarily to the bricks, not to the old mortar. If you put a thin layer over the old mortar, it will just flake off in a few months.
Never use a concrete mix between bricks. Brick mortar is specifically made to be softer and weaker than the brick itself. That way, if something moves a bit, the mortar will crack, not the brick. You can even get a latex mortar in a caulking tube for small jobs. For more details about working with mortar, click here.