Always spray fixative on the drawing and allow it to dry completely. Although the pencil drawing won't ever be in contact with the glass, this is a good precaution. Since the drawing sits behind the mat, there is the thickness of the mat between it and the glass. That's part of the reason for the mat, plus it looks good, too. Conversely, framing a pencil drawing without a mat allows the surface of the drawing to touch the glass, and it just doesn't look as nice.
Unfortunately, most artists don't concern themselves with frame sizes when they create their drawings. If you insist on framing the original art, be prepared to pay a premium for a custom size mat and a custom size frame. But if you have access to a computer with a scanner and an ordinary printer, there is a trick you can use to work around this dilemma. If you plan ahead, you can make it look spectacular without spending a ridiculous amount of money. If it's an original Picasso, by all means spend thousands of dollars on custom framing the original. If it's just a drawing that you would like to see on your wall, this is what I recommend:
Set your scanner at 150 ppi (pixels per inch). You don't need to go any higher than that, and you don't need to use photographic paper. You can get premium quality printing from an ordinary HP printer, like I have, with 150 ppi. By the way, the screen that you are looking at right now is 72 ppi, so the resolution will be twice as high as that. And since original drawings aren't done on photographic paper, they should be printed out on ordinary paper.
Anywhere that sells frames, such as Aaron Brothers or The Hobby Lobby, sells them in standard sizes. And they sell the mats in standard sizes to fit into those frames. So, if your drawing will look good in an 8 X 10 mat, you need to get an 11 X 14 frame. Please don't ask me where these standard sizes came from, all I know is that it is a whole lot cheaper to buy standard size frames and mats that to have them custom made. So you can pick out the frame you want and get the mat you want (with the beautiful bevel already cut), put them together, size your drawing on your computer, print it out, and put it all together. And that's the trick!
Something that can look even better, and be even cheaper than buying a frame and a mat, is to buy a framed print at a place like Big Lots. Just take out the print of the palm tree picture or whatever and replace it with your drawing.
Hang it up on the wall and it will look great!