First off, yes, it is physically compatible with your board (65W AM2 part). You might need to update the BIOS if your current BIOS was created before the Brisbane parts came out. According to ASUS's website (
http://usa.asus.com/product.aspx?P_ID=MnOfzTGd2KkwG0rF - click on the CPU Support List tab) you need BIOS version 1001.
You can check the current version of your BIOS by following these steps: (
http://support.asus.com/technicaldocuments/technicaldocuments.aspx?no=270&SLanguage=en-us).
If you need to upgrade your BIOS, you can download the BIOS and instructions from the first link I provided (on the Download tab).
As for the cooler, was your old CPU a dual-core or only a single-core 3800? If your 3800 was dual-core, you old cooler should be sufficient (they'd both be 65W parts). If you re-use the cooler, you will want to apply new thermal paste/grease.
If your old CPU was only a single-core, the old cooler might not be sufficient to cool your new dual-core CPU. If you bought a retail-version of the new CPU, it should have a cooler. If you bought OEM/bare/used, you might want to look into getting a new cooler just in case.
If you need help with the actual process, you can find many guides online.