I need advice on re stringing an electric guitar.?

Your description of your method confuses me but I will say this: needing to re-tune your guitar every week is completely normal, in fact, lots of guitars are notorious for needing constant adjustment, especially certain cheap guitars, and specific models like Telecasters. Now, if I understand the method that someone suggested to you, it sounds like a legit and useful idea. I, too, never used this, I did what you probably did for years. put the string in, and turn the tuning key until the string is taut. This works too. Try them both out. See which one is easier to do. See if one presents long-term issues, and the other does not. To be honest, guitar strings are generally inexpensive, and if you play your guitar frequently, you will have many a chance to re-string your guitar. My best advice has to be, that if you do not feel embarrassed at all, go into your local guitar place, or go visit your instructor, or your friend who has played for years, and ask them to show you how to string it, or my personal favorite, ask them to string it so you can see exactly how they do it. To be honest, though, I always put the string through the eyelet and turned the key until the string was taut. This always worked for me. I am also a bass player, and I might have different issues stringing my bass than you do your guitar. I am rambling. I hope this doesn't take too long to read. Good luck.

By 'bottom of the guitar', do you mean the bridge end or the headstock end? If it's the headstock end and there are metal bits near the edge, then you probably have a Floyd Rose. Those metal squares (you have three, right?) 'lock' the strings in place, so no matter how much you turn the tuners, your strings will always break. You have to unscrew them first. Guitars with a Floyd Rose are kinda hard to string. And it's even more complicated to explain. I suggest you let a pro do it or you run the risk of ruining the neck tension of your guitar -- not good. If you want to do it yourself, better keep an electric tuner handy. You WILL need it more than when you have an ordinary electric guitar.