たって is a casual structure that carries the same meaning as ‘ても’ or ‘でも’, and can be used with a wide variety of words. Common translations include ‘even if (A)’, ‘even though (A)’, or ‘no matter how (A)’.
In the case of verbs,
たって conjugates in the standard way that the た past-tense form usually would.
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彼女（かのじょ）に謝（あやま）ったってどうせ許（うる）してくれないだろう。
Even if I apologized to her, she wouldn't forgive me anyway.
先生（せんせい）に聞（き）いたって、何（なに）も教（おし）えてくれないからインターネットで調（しら）べる。
Even if I ask the teacher, they won’t tell me anything, so I am going to look it up on the internet.
For い-Adjectives,
たって attaches to the conjugative く-form.
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どんなに欲（ほ）しくたって、万引（まんびき）きをしてはいけない。
No matter how much you want something, you must not shoplift.
稽古（けいこ）がどんなに楽（たの）しくなくたって、稽古中（けいこちゅう）には欠伸（あくび）をしてはならない。
No matter how boring the lesson might be, you must not yawn during a lesson.
For nouns and な-Adjectives, た will change to だ, and だって will then be used with the stem noun or adjective.
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こんな簡単（かんたん）な問題（もんだい）馬鹿（ばか）だってわかるよ！
Even an idiot can figure out a simple problem like this!
友達（ともだち）だって喧嘩（けんか）をすることがある。
Even friends can get into fights.
Fun-fact - Although たって is widely considered a casual form of ても, it originally stems from たとて, which is a combination of the auxiliary verb た, and the particle とて, which itself is thought to be an old-fashioned abbreviation of と言（い）っても. In this way, the modern abbreviation of たって still reflects the original extended nuance of たと言（い）っても ‘even if (A) is said, (B)’.