Steps to Root your HTC Hero
1. Copy your memory card contents to your computer
2. On your HTC Hero, go to Settings > Applications and tick on Unknown Sources.
3. Go to Settings > SD Card and Phone Storage and click on Unmount SD Card.
4. Now click on Format SD Card.
5. Connect your HTC Hero to your computer using the USB cable, pull down the notification bar and click on the SD Card notification. Click on Mount.
6. Copy the downloaded FlashRec.Apk and recovery-RA-hero-v1.5.2.img files directly to the root of the SD card and disconnect your phone from your PC.
7. Go to the Android Market and download Linda File Manager or any other File Manager program.
8. Browse to the SD card folder using the file manager and click on the FlashRec.apk file to install it.
9. Open the FlashRec App and type the path to the recovery image in the text box -
Then click on the Flash Custom Recovery Image button and wait till it finishes.
10. Switch off the phone and boot into recovery mode by pressing the Home and Power button till it boots up.
Your HTC Hero is now rooted. You can now load and install custom ROMs if you wish.
Check out this article to see How to Install APK files directly on your Android Phone.