A travel experience

Today i will show you one of my travel experience.

show是给人看的意思。你这里是叙述，应该用tell+宾语+about:

Today I will tell you about one of my travel experiences.

还有，one of后面要用复数形式，因为是多个中的一个。

Last year,i went to Xiamen with my friend,by train.

Last year I went to Xiamen with my friend by train.

虽然很多人打字很马虎，但应该培养好习惯，就是I要大写，而且逗号、句号等符号后面要空个格。你的原句里的逗号可以用，但也可以不用。

We were ready from two city and we met in Xiamen.

不懂你的意思。什么叫we were ready from two city？ready是准备好的意思。还有，别忘记一个以上要用复数形式，即two cities。

That is my the first time i go travel alone.

my和the不能并用。然后动词的形式要符合时态，既然是过去的事情，要用过去时态。

This was the first time I travelled alone或

This was the first time I went travelling alone或

This was my first time travelling alone.

How excited!

这句又有问题。要么可以说How exciting!,就是多么令人兴奋的（就是形容这次旅行），要么说How excited I was!，就是我多么兴奋（就是形容自己）。你的原句不知道主语是你自己还是你那次旅行，如果是前者，一定要写出来，如果是后者，可以省略，但要用exciting，而不用excited。顺便说一下，exciting形容一件事情，excited形容一个人。interesting和interested、boring和bored也类似。很多中国人把这些词语混淆，要注意一下。