Combos occur from bonuses when killing enemies. Each type of bonus (sergeant, head shot, etc) will add an extra multiplier to the combo. An easy way to get this is to take damage link and C2C pulse when in a group. Damage link will give you points everytime an ally damages something else, and C2C will heal any damaged allies in range, also giving you points. Difficulty levels effect point values for enemies, so this might be easier for some on hard mode or above. Another easy way to get this is to be the last man standing, and begin raising your team mate as you continue to kill enemies.