How was year length first determined?

The length of a year was discovered long before the Romans.

And those ancients used much the same principles as we do to determine the true length of a year -- it's just that we have far more accurate instruments.

I think they would've used the stars to determine how long a year was, for example, the north star would be in the exact spot only once a year. But like the others said, the length of a year was discovered very early on, and nowadays it's all down to accuracy.

1. Mark the exact spot on the horizon where the sun rises. You can do this by marking a sstone and lining it up with a mark on another stone.

2. Wait until the sun rises again in that exact same spot, and that is one year.

You can do it with a star, too.
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It's pretty easy to notice the solstice dates, when the sun rises (or sets) farthest north (or south) on the horizon. Simple counting shows that these dates are 365 or 366 days apart, with an average close to 365.25 days. Keeping records for a few centuries show the average is closer to 365.2417. (The last digit changes slowly, so now it's 365.2416.)

Solstice dates have been celebrated for thousands of years. For many ancient civilizations that struggled to subsist through harsh winter months, the winter solstice marked a time of spiritual rejoice and celebration. Stonehenge was built before 2000 BC to observe the precise timing of the solstice.

Even back in 4000 BC, the Egyptians studied the apparent motion of the stars, to measure the difference between the 365.25 day "tropical" (solar, or cycle of the seasons) year, and the "sidereal" year (which is about 20 minutes longer than the tropical year). The difference seems small, but it adds up to a whole day in just 71 years, and 10 days in 710 years.

By the way, in 1582 the Church was more interested in the March equinox dates, so they set up a calendar with an average of 365.2425 days, about as close as they could come to the correct value of 365.2424.