Blackholes can't be investigated. They are impassable terrain that may hold Antimatter resources. You need to build a starbase near the resources and upgrade it with a mining ring to harvest those.

If you are actually referring to wormhole anomalies, you need a ship with a survey module to investigate them.

Are you playing the basegame tutorial or the Crusade tutorial?

I just checked the Crusade one and it asks to survey an artifact anomaly. You most likely mistook wormhole for blackhole.

Select a survey ship and then right click an anomaly.