Learn Dutch: Aan de hand van de doelgroep bepalen wij het segment. - Using the target group we determine the segment.

Literally, it means "at the hand of." Idiomatically, it is a highly common set phrase meaning "on the basis of," "by means of," or "using." It indicates the criteria or reference material you are using to make a decision or complete a task.

How does aan de hand van compare to uit (as in blijken uit) when discussing sources?

While uit points to the direct origin of a fact or piece of evidence (like a report or survey), aan de hand van points to the guide or criteria you are actively using to figure something out. You learn a fact uit a report, but you make a determination aan de hand van a set of data.

Could I just say met de doelgroep to mean "using the target group"?

You could, but aan de hand van is much better suited for professional or academic contexts when you mean "guided by" or "based on." Using met (with) often sounds a bit too literal or physical, as if the target group is a physical tool.

Why is the verb bepalen placed before the subject wij?

This is a standard inversion triggered by the V2 (verb-second) rule. Because the sentence begins with the long prepositional phrase Aan de hand van de doelgroep, the conjugated verb (bepalen) must immediately follow it to stay in the second grammatical position, pushing the subject (wij) right after the verb.