Here's some advice.
1) stick to the main Shadowrun 3rd Edition standard rules for a couple months. Don't use Magic in the Shadows, or Cannon Companion, or Man and Machine expansions.
2) Players should use archetype characters (Premade characters in the main book; pictures start on page 65; real data starts on page 326) until they've played a couple months and have an idea of what type of character they'd like to play long-term.
3) GM should ignore all Rigging (vehicle activity and combat) and Decking (computer activity and combat) for at least 6 months. If your adventure requires rigging or decking, tell the players that you're doing a simplified version of it to improve speed of play, and just have the character roll 6 dice. If they roll better than average, describe a better-than-average result, and so on. Learn Rigging and Decking after you have everything else covered.
4) Practice a combat-only session with all the players before starting an adventure. Take your time, and work out how it works. Learn about Initiative, Combat Turn, Multiple Actions per Turn, Complex and Simple Actions, Movement, and Damage. Learn about penalties to actions (cover, wounds, vision, movement, recoil) all in the practice session.
5) Describe for your players what their characters know of a "Typical Shadowrun", as they have previously experienced or heard from other shadowrunners. It has "the meet" with "Mr. Johnson" (always Mr. Johnson), the pay (often half up-front), the legwork (finding out things) and the planning, and finally the execution of the run, making delivery (if needed) and final payoff. Describe the notion of "professional" shadowrunner, who knows that generating a good reputation is needed in order to get higher-paying jobs in the future. Describe the notion that a "team" is needed, because the world is so complex and no one can do it all. The most successful shadowrunning teams have a variety of skills, they back each other up on skills (who treats the medic if he goes down?), and they trust each other with their lives and expect the others to do their job.
6) You can look up rules as you go during your first game (slow but sure), or you can wing it, using your best recollection of the rules and keeping the pace fast and tense. Do whichever works for you.
7) If you can find an experienced GM anywhere (convention, local game store), ask him to help you. He might GM the first time, or run the combat practice session.
8] Magic is an integral part of Shadowrun, but it's possible to do a couple Shadowrun adventures without any magicians on your team or on your opposition. The Magic rules add a whole new dimension to the game (astral scouting and surveillance, invisibility, clairvoyance and fireballs, to name a few). If you and your players can play two or three times without any magic, that'll simplify things to start with.
Here are more suggestions, in a previous thread titled
GM Advice.