Paradise
noun
This place has extreme comfort. It is paradise. 極楽 is a short for 極楽浄土 (the Pure Land in Mahayana Buddhism). While it might sound a bit old-fashioned, you can still use it to describe something heavenly. For example, if you're soaking in a cozy, relaxing hot spring, you could say, "Ahhh…極楽!"
ごくらく
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well. 極 has two on'yomi readings, though. So here's a mnemonic to help you remember which one to use: In paradise, you meet Goku (ごく) from Dragon Ball Z. He grins and tells you he's taking a break from extreme battles and enjoying the extreme comfort of this heavenly paradise.
温泉に入って極楽気分を味わいました。
I entered the hot springs and felt a blissful feeling.
悪いことをしてたら、極楽に行けないよ。
If you do bad things, you can't go to paradise.
間違いで極楽に行った男についての小説が、映画化されました。
The novel about a man who went to paradise by mistake was made into a movie.
「極楽とんぼ」とは、事の重大さに気づかず、のんきに構えている人のことをあざけて言う言葉です。でも、今では芸人さんのコンビ名としてしか知らない人がほとんどですね。
Gokuraku Tombo (dragonfly in paradise) is a term used to mockingly describe people who are unaware of the seriousness of a situation and take it lightly. However nowadays, most people only know it as the comedy duo's name.