Update, September 2016:
I’m not sure this is still relevant, or why it’s getting so many hits. It was written nearly five years ago. If you’re on a modern build of MIUI and search is broken, chances are this isn’t the solution.
One of the major problems of MIUI is that landscape support is nonexistent in the home screen and, more importantly, the search app. I have a hardware keyboard, dammit, let me search properly!
The obvious solution here is to install a sane search app – like Google Search. However, the search button will still run MIUI’s search app. The fix for this is, as a quick web searching session will reveal, to convert Google Search to a system app.
But how do you do that? The tips you’ll find on the Web will probably suggest using Titanium Backup (which lets you do that in the paid version) or, deities forbid, some Windows app and a 20-step guide. However, there’s a much simpler solution:
- Get the Apps2ROM app and open it.
- Scroll down to Google Search, tick the checkbox next to it.
- Tap the “Save” button.
- Tap the “Move now” button.
- Agree to the restarting of your phone.
That’s it. No payments and no PC involved.
Abandoned Blog 
I have found this and it work!
To change, open up browser, then press menu button, then tap Settings, then tap Advance, then tap Set search engine.
Do you think I can use Apps2ROM with a dual boot kernel ?
I use MIUI like secondary ROM with Siyac kernel.
This worked flawless, thank you! Lost search button to MIUI search after the app updated in the market, but this brought it right back! (EVO 4g MIUI 1.11.1)