1.Let me introduce myself.让我来介绍我自已。
introduce，v.介绍。常用于结构:introduce sb.to sb.，把某人介绍给某人。
She often introduces her friends to her sister.她常把她的朋友们介绍给她妹妹。

2....I am trying to use some new words.
.我在努力用一些新单词。
try to do sth.，努力做某事。try doing sth.，尝试做某事。
The girl tries to study hard at English.这个女孩努力学习英语。
Can you try helping him?你能试着帮帮他吗?

3.I'm looking forward to your reply.我期待着你的回复。
look forward to，期待。to为介词,后面要跟名词/代词或动词-ing形式。
to作介词短语的还有:
listen to听;be used to习惯于做;pay attention to注意。
l look forward to seeing him again.我期望再次见到他。