There is a specific module that you have to put on a ship to give it the ability to survey and therefore explore anomalies. In a normal game, your flagship, which is given to you from the start, has survey capabilities eventhough you do not have the requisite technology to build one yourself yet. Once you have the requisite tech, you can build a survey vessel yourself.

There is also a building you can build later that will give all of your ships the ability to survey at no additional cost. I can't remember the specific tech you must get to get this off the top of my head.

First you need to research sensors.
Than you can put a survey modul to your ship designs.

edit: Seems I was to slow....