(I went to/am going to/will go to)airport to pick up my brother.
There's no tense in Chinese,when this situation happens depends on the scene which the speaker is talking in.
到means arrive at. the meaning of this sentence is similar as the first one.
I have picked up my brother at the airport.
so 到means you have finished this action and the result is you brought your brother back.
Another point that I want to remind you,
(please answer me a question)
(let me ask you a question)