I think this sentence is correct.
I done something.
This is also correct.
I have done something.
What are the involved tense? How are they different?
"I done something" is not correct. You should say "I did something."
"I have done something" is correct.
"I did something" is simple past tense. It means you performed the action at some time in the past and it is now complete.
"I have done something" is present perfect. It indicates that an action that began in the past and continues into the present, or whose effects continue into the present. It can also be used to indicate an indefinite time.
"I wore a green shirt." I did it at some particular time in the past.
"I have been wearing a green shirt." I put it on in the past and I still have it on, or I regularly wear it.
"I have worn green shirts." I have done this at some unspecified time in the past.
I done something” is not grammatical. The verb form done is a past participle. A participle cannot have a subject (I).
A participle can be part of a compound verb form, such as perfect aspects (see below) or the passive voice (“Something is done by me”). The other main use of past participles is as adjectives; this is relatively uncommon with done because it gets so much use as a verb and auxiliary, but it can happen.
“I have done something” uses a present perfect. The present perfect is formed by taking the present tense of the verb have and adding the past participle of the verb.
The present perfect is one of the two main past tenses in English. The other one is the simple past (also called preterite): “I did that”. It can sometimes be difficult to know when to use a present perfect and when to use a simple past, but there is a general rule:
Both of these forms also have continuous forms (“I was doing”, “I have been doing”) which are used for actions which are ongoing, i.e. that lasted for a period that is longer than what the sentence is about.
I worked in London from 2001 to 2004. [specific point in the past]
I was working in London when I met my wife. [interval during which something happened]
I have worked in London, I know how bad the commute can be. [happened in the past, but the moment is unimportant]
I have been working in London for five years. [happened in the past and still happening now]
Using the past participle instead of the preterit form, as in “I done something”, is something that some natives do and that you should not imitate. It is associated with several popular or vulgar variants of English. In some circumstances, it could make you percieved as uneducated or uncouth, or worse, be interpreted as a mockery. That's very dependent on the context, of course: if you say it with a recognizable foreign accent, it'll just be interpreted as a foreigner's mistake.
The first is not correct. It should be "I did something."
The first sentence (when using did instead of done) uses the Simple Past, the tense used when talking about something happened in the past.
The second sentence uses the Present Perfect, the tense used when talking about something happened in the past, which is still relevant for the present.
To understand the difference, consider the following sentences.
I was home.
I have been home since 3:00 PM.
The first sentence says I was home at some time in the past; the second sentence says I was home at 3:00 PM, and I am still at home.
With the sentence you used, the difference between I did and I have done is that the second is putting the accent on the fact that what you did is still relevant for the present. Probably, in American English most people would use the Simple Past.