高兴 (gāoxìng) is the everyday word for 'happy' — the most common way to express feeling glad. 快乐 (kuàilè) suggests deeper, lasting joy; 开心 (kāixīn) is similar but more casual. 高兴 also means 'willing' (as in 不高兴去 'not willing to go'), but for that meaning 愿意 (yuànyì) is the standard verb.