@revv You are on the right track theory-wise with the battery, two coils, and an LED. Unfortunately, from a practical point of view, the coil connected to the battery will look like a dead-short and will quickly drain the battery. Your two coils are probably not tightly coupled together, magnetically, so not much energy can be exchanged, even in the best of circumstances. Not enough voltage or current will appear in the coil with the LED attached to it. Finally, an LED is not a very sensitive indicator devices. It requires "considerable" current... a few milliamperes... and significant voltage... a volt or two before it "lights up". You need an analog device called a galvanometer. Not to worry, you can make a serviceable one quite inexpensively. Read on.
What it appears you are doing is trying to demonstrate a practical example of Michael Faraday's experiment, where he discovered (almost by accident!) magnetic induction.
Go to this Google results page and look at some of the pages linked there to get started learning about this fascinating aspect of electronics.
And while I am here, this reminds me of an incident that occurred while I was in in grade school. The teacher was doing science one day, and we were supposed to be learning about electromagnets. For homework, she told us to go home and find some copper wire, a large nail, and a dry-cell battery and wind our very own electromagnet. In those days, a dry-cell "battery" would typically be a 1.5 V cell with thumb-screw terminals on one end. These were often called "A" batteries when several were connected in series to light the filaments of battery-operated tube-type radios. Anyway, they were still fairly common, although expensive, in the 1950s when this story takes place.
So the next day we all show off our "electromagnets" in class. I think we shared the batteries because some students in my class could not afford to purchase a battery... not even a "D"-sized flashlight cell. One such unfortunate couldn't afford to purchase insulated copper wire either, but he was resourceful enough to find some bare copper wire on the farm where he lived. I have no idea what bare copper wire is used for on a farm... electric fence maybe? So he also finds this humongous nail in the barn and proceeds to wrap it with the copper wire he found. It was quite an impressive hunk of metal when he finished and showed it to us in class. So we loaned him a battery to try it out. Alas! The hunk of bare copper wire got warm, the connecting wires to the battery got warm, and the battery itself got warm when it was all connected up in a circuit, but there was no magnetic field produced in the nail! What a disappointment this was to the young boy. He thought he had done everything right, but somehow the idea that insulation on the copper wire was important flew right over his head.
So,
@revv I hope when you wrapped your wire around the nail you remembered to use insulated wire. There are lots of other things that can cause an experiment to fail, but using bare copper wire to construct magnetic coils only works if the turns of wire don't touch either each other or touch a conductive form (like a nail) on which they are wound.
In my youth I found that it was a lot of fun to try to reproduce the experiments conducted by the 19th Century pioneers in electricity and electronics. I was without equipment, but a simple galvanometer can be made with a pocket compass (the kind that has a needle that sorta points toward north) and a few hundred feet of insulated fine wire. Or, even easier, if you can find a largeish loudspeaker the so-called voice coil can be removed. You just place the compass on a level surface, place the compass inside a coil so the turns of coil wires are crossing over and under the compass (not around the needle axis!), and then orient the compass so the needle points perpendicular to either open end of the coil.
Now, if a small current flows in the coil, it will produce a small magnetic field that will deflect the magnetized compass needle from its preferred north-south orientation. If enough current flows, the needle will deflect ninety degrees away from its preferred north-south orientation. So build this, lock it down to the table so it won't get disturbed after you get the compass oriented properly, connect with some flexible wire the coil that had the LED attached to it, and go explore the magnetic field created in the first coil you connected to the 9 V battery. Hint: it helps to wind a
lot of turns of wire on the coil you connect to the 9 V battery. Even so, that battery is going to die pretty quickly. Best to find and use a current-limited DC wall-wart to play with instead of a battery.
Hop