There are two ways to circumvent it, one way will make it impossible for you to go on live without getting banned, and the other will allow you to play burned games.
Here I will explain the 3 different way to "hack"/"mod" and xbox360 and you can decide which is better for you.
The quick run over of the three:
Jtag and rgh - both are means to exploiting the xbox360 and allowing the ability to run unsigned code, AKA homebrew apps. What it basically does is allow you to get root access to the xbox and run games off your hard drive and run emulators and xbla games all for free.
while flash AKA FW AKA firmware is a mod to your optical drive that allows you to play burned games. the down side to flash is that you can only play them off of dual layer discs that need to be burned from a specific disc drive. more information at junglefalsher.net the upside is that you can play on live and hopefully - though it is still possible - not get banned.
Look at your power input on the back of the xbox, if it is a slim, if it has 9.86 amps then it is the corona motherboard which at this time isn't able to be glitched. If it's the old white xboxes, all you need is to make sure that it has HDMI Check this picture out: http://www.team-xecuter.com/psu.png.
As for deciding what you want to do you need to decide what is best for you. Do you use xbox live a lot? If so you want to go with fw flashing. If you don't use xbox live a lot and want homebrew apps/emulators as well as XBLA games, DLC, Avatar items, and being able to run games from your hard drive, then RGH/jtag is a much better option for you. Or you can have both with a dual boot system.
What you're going to need for the FW flash hack is a way to unlock your drive so you can flash it, using a team xecuter product is your best option and to find all the tutorials on how to do a fw flash go to jungleflasher.net
For RGH you're going to need to solder a chip - a cpld - into your xbox so that it can glitch the cpu and allow you to boot into a hack operating system. The best chip on the market is the Team Xecuter Coolrunner. They are actually going to be releasing a new chip here soon with the built in dual boot. For all your tutorial needs go to team-xecuter.com. Also you will need a nand-x, it's a tool that allows you to read the xbox's NAND and program it, as well as program you CPLD chip.
For dual boot at this moment the only chip on the market is the cygnos chip. It is a lot more programing and soldering.
The Jtag hack is less expensive because it is actually a software based exploit rather than a hardware based one and the tools needed are cheap and can be picked up at radioshack. check out http://www.boxxdr.com/boxxdrjtag.html for the tutorial on the most efficient way of doing the jtag hack. One of the downsides to the jtag hack was that it was patched by microsoft and any dash newer than 7371 can't be exploited through the jtag hack, only the RGH hack
You x360key which is an ODD -optical disc drive - emulator. It basically emulates the disc drive and plays games through a jump drive or hard drive. It's okay, but isn't efficient for the money you shell out you could easily pay someone to do the RGH and have a lot more functionality.
I do these hacks a lot for money and everyone is very pleased with my work. I would not suggest you attempt any of this without a lot of research and practice on a dead motherboard. You basically need to solder a ball on to the E of a penny. If you want more information or help email me at dahlonl@yahoo.com I am always up to helping people out. Also if you're just looking at buying another xbox I have brand new xboxes never been used that I'm selling that are completely ready to go.