The current version of the iBooks app requires iOS 5+, so if you don't have that installed (your current version is shown in Settings > General > About > Version) then you will need to update it, and you should then be able to install the app.
To update, connect the iPad to your computer's iTunes and copy any purchases off the iPad to your computer via File > Transfer Purchases (File > Devices > Transfer Purchases on iTunes 11). You may also want to copy photos (e.g if you've saved any from websites and/or used the camera connection kit) and any important documents off the iPad as well e.g. via the file sharing section at the bottom of the device's apps tab when connected to iTunes, via wifi, email, dropbox etc - they should be included in the backup, but it's best to have a copy of them outside of the backup just in case. You can then force a backup of the iPad by right-clicking the iPad 'Device' on the left-hand side of iTunes and selecting 'Backup'.
Then start the update by selecting the iPad on the left-hand side of iTunes (on iTunes 11 you can enable the left-hand sidebar via option-command-S on a Mac, control-S on a PC), and on the Summary tab on the right-hand side clicking the Check For Updates button
Updating to iOS 5+ : http://support.apple.com/kb/HT4972
A first gen iPad will be updated to iOS 5.1.1, which is the only version that is 'signed' by Apple for it.