The red wire probably attaches to the positive connection in the pill, but you never know, they may have actually used a red wire for negative... So please answer the following:
1) How many batteries does the laser use and what type AA, LiIon
2) Which way round do the batteries go into the battery tube - This is really important.
Please also specify the wavelength of this laser 405 or 445, blue is rather nondescriptive.
If the batteries go in positive first then strip the tip of the red wire and connect this to the positive pole of the battery. If you usually need 2 batteries put 2 in series (ie end on end) and touch the negative pole of the second battery to the exposed threading on the host end where the red lead is still attached. If you normally use one battery use only one battery and connect the positive lead to the battery positive pole and use the neg from the same battery to the case.
If the batteries or battery go in neg first then connect in the opposite way ie red lead to neagative and positive on battery to the case.
If the laser turns on you just need to resolder the wire :beer: