Most of the time putting the needle in backward does not actually hurt them machine. But it can cause the needle to jam in the hook assembly. The really damage comes when too much force is used to try to get that needle out. I have had luck in loosen the screw in the needle bar that hold the needle in place and then carefully rocking my fly wheel back and forth while holding the needle with with a pair of pliers. I put a slight upward pull on the pliers so that the needle will come up when it gets to a point it is loose enough to move. I have actually had to do this several times to other people's machines and have not had to time the machines afterward. It is a really good idea to check out your stitches on practice cloth, if you ever make this mistake. After all, it is better to find out you have an issue there then on a quilt where you have to pick out stitches. Also if your machine ever jams, turn it off immediately. Just turn the power switch off. There are worse things then retiming... Actually retiming is not as bad is it's reputation would have you believe. It is more fiddly then hard.
When you look at your needle one side will have a long channel that runs all the way from the eye to the the top of the shaft that is inserted into the machine. The other side has a concave area that is about as wide as my index finger, shown is the slightly blurry picture above. The channel faces toward you when you put it into the needle bar, the concave area faces the back of the machine. The channel is designed so that you can slide the very end of the thread down the channel and straight into the eye so it makes sense that have to be able to see it when you are threading the needle. I normally cant my needle ever so slightly to my left. So that the eye is at about the 35 minute mark if straight towards me is the 30 minute mark. This helps when you are using finicky threads. It gives the hook a little bit longer to catch the thread when it is spinning. I use a very thin pin to show me how my needle is orientated and then use it to hold the needle all the way up in the needle bar as I tighten the screw. I use a flat headed screw drive with a long handle as that give me more torque and I really tighten that little screw. The last thing I want is that needle getting loose and falling out and down into my hook. This is one of the few places that I "boy" tighten a screw on my machine.
I actually use the channel ever time I thread my needle. I tickle or flick the end of the thread across the front of the needle (left and right) when it catches in the channel I just slide it down and through the eye. It is the fastest why I have found to thread the needle. If you watched me do it you would think that I was just sticking the thread directly in the eye of the needle. I would notice immediately if my needle was backwards because it would be harder to thread the needle.