The ancient Greeks wrote the same way as the Egyptians: on papyrus scrolls. The oldest European manuscript I know of is the Derveni papyrus which is a Greek scroll dated to 362 B.C.. The writing was made with a narrow brush rather than a pen. The Greeks also wrote on clay, such as the fragments of broken pots (ostraka). Students would write on the ground or on wax tablets which were a layer of beeswax recessed into two boards which had a thonged hinge, so they could be closed together:
The wax was engraved with a pointed wooden stick called a stylus. The reverse end of the stick had a spatula which could be used to erase, as can be seen in the image above.
The writing on papyrus was relatively slow compared to using a pen, because it was brushed on. This was unimportant though, because when something was written to papyrus (very expensive) it was usually an important work, so the amount of time taken to write it was not important. If they wanted to write notes or something fast, wax would be used, which was reasonably fast. In some cases charcoal was used to take notes on a convenient surface like clay or stone.