To shine your hardwood floors you should first go over the hardwood floors with some vinegar or Pine Sol to get them as clean as possible.
To clean hardwood floors you can use some Pine Sol added with some mop water and then wring out the mop good enough to avoid getting too much water on the hardwood floors.
You can also use vinegar in a bucket of mop water to clean your hardwood floors and I sometimes use the Pine Sol and other times I use the Vinegar to clean the hardwood floors.
Just don't allow the hardwood floors to stay too wet otherwise you risk cracking or warping the hardwood floors.
So wring out the mop good before mopping the floor with it.
Vinegar is a very natural way of cleaning hardwood floors and other surfaces but Pine Sol is great for cleaning hardwood floors too.
Then to shine the hardwood floors you should use some lemon essential oil into the vinegar which helps the hardwood floors naturally shine.
Or you can use some Pledge Floor Gloss that you can buy at Walmart that does a great job at getting your hardwood floors to shine.