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LingakuLingakuてから means "after doing ~". It goes after the て-form of a verb, and the first action is finished before the second one starts.
When the first action has a subject of its own, that subject takes が.
A plain て-form also links actions in order, but it only lists them. てから says the first one has to come first, so it is the form for when the order matters.
With ている or a change in the second half, てから is "since": from that point up to now.
The two look alike. から after the た-form is "because", not "after".