They resemble a pair of records floating on rotating gears. By scratching the records, he is able to control the flow of time in a variety of ways. He seems to be able to use standard time travel to go forward and backwards in time and uses this ability in battle.
He mentions to Alternate Future Rose that he's spent four months skipping back and forth. After returning to the main timeline, he gives the timetables to Present Dave before jumping into the sprite. [Source: wikia]
You can download the papercraft templates here: MS Paint Adventures - Dave's Timetables Free Papercraft Download