中文(简体)
Chinese Self-Introduction Phrase: "很高兴认识你"
"很高兴认识你" (Hěn gāoxìng rènshi nǐ) is the standard Chinese way to say "Nice to meet you," literally meaning "I'm very happy to know you." It's natural to say right after introducing yourself. You can reply with the same phrase, or "我也是" (Me too).
Examples
我叫小明。很高兴认识你。
"My name is Xiaoming. Nice to meet you." (a common thing to add right after saying your name)
我也是，很高兴认识你。
"Me too, nice to meet you." (a typical reply to "很高兴认识你")
久仰大名。
"I've heard so much about you." (a slightly formal phrase used when you already know of the person's reputation)