LG Optimus 2X is fairly the best smartphone I've used. Although some users are facing issues, and are not satisfied with their device. Here are few tips, which can help you increase user experience of your brand new dual-core monster.
1. Check if your software is up-to-date
Some units of O2X were delivered with early builds of software and were not always stable. If you are facing random reboots, one of possible reasons for that may be old firmware.
The baseband version is also important - users who reported bad audio quality during phone call confirmed, that update solved their problems.
Be sure that you are using the latest version of software (current is v10D).
You can always check for updates with LG Mobile Support Tool.
2. Replace the stock launcher
Your O2X is not enough smooth? You can't stand that switching between homescreens is not fluid?
Repleace crappy LG Launcher with other app! Just visit Android Market and download one of the few popular 3rd party launchers, like LauncherPro or ADW Launcher. You can also try stock Froyo/Gingerbread launcher.
3. Remove bloatware
O2X comes preloaded with several additions from LG. While some of them are really handy, few others are not at all, and are only wasting resources.To remove them, you will have to root your device, which is a piece of cake, and this operation can be reverted with ease.
After you gained Superuser (root) access, download for free TitaniumBackup from Market.
Than click on the app which you are sure is not important (for example: F-Secure, CarHome, widgets), and select "freeze" (or "uninstall" if you are 100% sure).
4. Stop using task killers
There were several articles about why using task killers in Android is pointless, I won't talk about it.
Just believe me that you don't need it, and it only makes you feel that the device is unresponsive.
Instead, try AutoKiller from Market (root needed) and select "Optimum" preset - it will help system with managing background apps and leave you with more RAM free.
5. Install MoDaCo Custom ROM
If you are enough advanced user, go and take a look at MCR by Paul. It's the best custom ROM at the moment of writing, and comes with set of customisations and tweaks which will increase performance of your Optimus 2X.
If you will donate MoDaCo, you will be able to use online kitchen and easily bake ROM which will suit your needs. But you don't need to do that to use MCR, there is always prebake available - the downside is that it comes preloaded with apps you may find not useful, so you will have to take a look at part 3. of this tutorial.
You can download the latest version of MCR here.
If you have any questions, leave them in comments, I'll take my time and try to help you :)