Just as there are different ways to wish people on their birthday using English, there are also different ways you can go about this in Italian. The common translation for "happy birthday" in Italian is "Buon compleanno." You can see this is a combination of two Italian words; buon means "good" while compleanno means birthday.
For people who speak Italian, they definitely won't find it difficult to pronounce the two words, but for nonspeakers of the language, you can easily pronounce the two words by saying bwon kom-pleh-ahn-noh. If you are able to pronounce this, you are already saying happy birthday in Italian.
Most people scream when they use this expression to wish their friends on their birthday. At times, the Italian expression "tanti auguri! " is used to wish people on their birthday, though this expression doesn't mean happy birthday, but can still be used to wish people on their birthday since it means "best wishes."