Let's start with the fact that today's glass isn't really colourless - if you look at a thick pane of glass, or from the edges, you'll notice quite a green tint. This is a big deal in showcase aquariums, where many of us prefer so called low iron glass.

Glass is basically melted sand, which is usually composed mostly of silica. Depending on the rest of the chemistry, you'll get different impurities. So the Greeks would have used the sand from the nearest beaches, as would the Romans and the various people through the middle ages and on down the line.

It all would have started with glass beads being made by accident during metal work, which wouldn't even have been clear because of all the impurities. Over time, people figured out more ways to refine it until we ended up with mostly clear glass.

The Italians in the 15th century started making super clear glass called Cristallo out of quartz, and by selecting against any colouration, ended up with a very pure silicate. Unfortunately, this also led to quality issues. This would have been used for finery, but was still a rare thing, and the rest of the world marched on with gradual improvements.

The low iron glass we use today uses a sand that's low in iron naturally. To be clear (heh) though, this still takes more refining than the Romans had access to.