For those who don't understand what this is about.
Old Baseband = If you have the Stock Froyo (2.2) Android system on your phone then you have the OLD BASEBAND, and you do not need this unless you updated to past 2.2.2 then continue reading if you wish to root your phone the easy way.
New Baseband = If you updated to the Stock Gingerbread (2.3) Android System on your Optimus One, then you fit this category, Lg have implemented a new baseband in this update which makes any Roms based on the old baseband not function, as well as making it more difficult to root your phone
FLASHING OLD BASEBAND
If you're already on official Gingerbread version you will need to downgrade your version to Froyo 2.2.2 using KDZ Updater. This is because the new Gingerbread contains the new baseband, and the Froyo firmware is the old baseband.
To do this please go onto this link that contains kdz and the stock Froyo 2.2.2 Rom required to flash. The reason you need 2.2.2 is its the easiest and proven version to work with Gingerbreak to root your device.
Notice: If by some ACCIDENTAL reason, your phone gets stuck in EMERGENCY MODE during flashing, follow the instructions on this link how to use KDZs functions to continue flashing the firmware you downloaded in Emergency mode.
FLASHING NEW BASEBAND
The Kdz File for new baseband is below, use the same method as above only using the v20G .kdz file instead of the 2.2.2 v10E update.
This will update your phone to the official LG 2.3 firmware, in which the new baseband originated.
If then stuck on LG Logo OR boot animation, try pulling and putting in your battery, turning on your phone and holding down volume down and home key, this should reset your phone to factory and then you will be able to boot into the stock gingerbread.
The easiest way to get root privileges on Old Baseband (2.2.2) firmware device is by using Gingerbreak apk. Just download it, install it and run it.
To get Root access on the New Baseband (2.3.3) use SuperOneClick
Or direct link to the latest version
Make sure, after you download the program, you go into your cmd, then go into the ADB folder, drag the ABD exe file into command prompt, delete the .exe part and add devices, so it look like this
Download the ADB.zip attachment on this post, EXTRACT it so cmdXP and cmd7 are located inside the ADB folder in the Superoneclick directory, and run either version, depending on your windows version (This links you directly into ADB app, instead of manually dragging ADB.exe int cmd, really its just for your convinience.)
Then all you have to do is type the following lines.
then type in the following directly after
echo 1 > /data/local/lge_adb.conf
Then go into Superoneclick.exe, select auto method and run root, this should then eventually root your device.
Some Antivirus softwares will detect Superoneclick as a Virus.
IT IS NOT A VIRUS, just the types of exploite code it uses makes some antivirus software think of it as malicious. Just disable your AV for 5 mins before you extract Superoneclick.
There's two popular custom Recovery versions for O1 - AmonRa and ClockworkMod
The easiest way to flash ClockworkMod Recovery is by downloading ROM Manager app from the Market (free or donate version doesn't matter) and choose to flash the latest recovery version and choose the option to Reboot in Recovery mode.
For Other Recoveries including Amonra there are a few links, but here is the one that has flashable zips
Just flash the zip files in Clockworkmod recovery menu, after you install that through Rom Manager if you wish to use a different recovery.
Now that you got the right baseband + your device is rooted and loaded with a custom recovery you may install any Rom you wish that is based on the correct baseband such as
Mik_os 6.5.8 Cyanogenmod port (OLD BASEBAND).
[UNOFFICIAL][DEV/GEEKS-ONLY] Cyanogenmod 9 (Android 4.0.3)[BETA][NEW BASEBAND]
OFFICIAL CYANOGENMOD Rom [NEW BASEBAND]
Oxygen ROM 2.3.2 (Android 2.3.7)[NEW BASEBAND]