You will need the LG Optimus V drivers on your PC, they are found here
http://www.lg-phones.org/wp-content/uploads/LG-Optimus-V.zip (you phone cannot be plugged into the PC when installing the drivers). Once installed reboot your PC.
To set up ADB in you PC's system path go here
New pre-packaged ADB installation
This is fool proof and has worked 100% of the time.
If you don't have a custom recovery installed (if you only have 4-5 options in the recovery instead of 8-9 options you don't have a custom recovery)you will need to put it and the flash_image on the SD card as well as the ROM and Gapps. Turn power to the phone off and then pull the SD card and install on a PC.
Go here
flash_image
Then go here
BobZohme modified CWMod recovery (VM670NH_recovery.img) Rename the recovery to recovery.img
Download the BACKside ROM found here
http://androidforums.com/optimus-v-...wip-backside-rom-cm7-green-machine-theme.html and the 2011828 gapps found here
Latest Version/Google Apps - CyanogenMod Wiki
Then put everything on the root of the SD card(not in any folder, just near the bottom of the list of folders).
Put SD card back in the phone and then power up and plug phone into the computer. Wait for the drivers to finish installing.
Open up a command prompt and type in each line of code making sure you hit the enter key after each line:
cd..
cd..
cd SDK/platform-tools
adb shell
(You should get a #). If you don't get a # but got a $ instead type in:
su
(you should now get a #). If you did not get a # put got a $ after, you are not rooted.
You will need to go to the link that andrewnelson32 posted.
If you got a # then go here
http://androidforums.com/optimus-v-...ry-reset-your-rooted-phone-3.html#post3263770 Go to step 6a. and start with line #2 and go all the way to step 9.
EDIT: If you have a custom recovery installed use the recovery that kwknott provided below.
Make sure you put the ROM and Gapps on the root of the sd card as well. Install it on the root of the SD card, but leave it zipped. After putting the SD card back in phone press Home+Volume down then power button(hold down all at the same time), when you see the LG logo you can let go.
Then in the recovery menu select "install zip from SD card". Then "select zip from sd card". Select the recovery.zip. After install hit the back button and scroll down to the advanced section. Select it and then select "reboot recovery". This will boot up into the new recovery.
Then go into the advanced section and select the "fix recovery loop" option. Hit the back button.
once in the recovery's main menu follow step 7. in my tutorial I linked to. Follow it all the way to step 9.