Gin and tonic=rocks glass, filled with ice, one shot of gin, fill with tonic, garnish with a slice of lime
Now, obviously, a rocks glass isn't very much to drink, but that's the standard that you get if you order it at a bar. The way it works out is something in the neighborhood of 1 part gin to 2 parts tonic, or so, and the first time I'd keep that ratio to see how you like it. If it's not strong enough, go closer to even portions. If it's too strong, move in the 1:3 direction.
I always squeeze my lime into the drink and stir (and then boorishly eat the thing after I finish off the drink). Other people will just rub the slice on the rim of the glass so they get a hint of lime as the drink goes down. There's not really a "correct" way to deal with the lime. The drink ought to be served with a slice of lime. What you choose to do with it (eat it, squeeze it, throw it away, squirt your date in the eye), is really up to you.
I guess this bears saying: drinking should be something that you do in a way that relaxes you and that you enjoy. If you don't like how a drink recipe makes something taste, for the love of god don't do it. Tkae the parts of recipes you like and keep them and toss the parts you don't like. Mess with amounts insofar as you're comfortable messing with them. Unless you're a bartender and you're trying to conform to the preferences of other people, don't worry about what the norm is or what the recipe says, just make what you like to drink how you like to drink it.
And, having been a bartender, no matter what you think a long island iced tea is, you're wrong, and people will be happy to tell you how you're supposed to make it.
