We use "was" with I, he, she, it when speaking of the past: it is the singular past form of the verb "to be". We use "were" with you and they and we: it is the plural past form.

But sometimes we can use "were" with I (he, she, it):

I wish I were a sailor.

Here, I've expressed my wish to be a sailor, which I am not.

This is called the subjunctive mood, used to express desires, wishes, intents. It is used to talk of "unreal" situations (that we wish were real).

This is the only instance in which we can use "I + were", and in modern English you can safely use "was" in its place, both sentences will mean the same:

I wish I was a sailor.

An example of use of "I + were", from a song:

If I were a carpenter
And you were a lady
Would you marry me anyway?
Would you have my baby?

Here, the singer is not a carpenter, he merely speculates what might happen if he were to become a carpenter (or "if he was to become a carpenter", which is the same).

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If I were you and wished to know more, I would read up on the subjunctive mood in Michael Swan's Practical English Usage, Topic 567.