Use statistics!
You can't count to 60 and expect it to be a minute. You cant sleep one night and think you got a perfect 8 hours.
But you do have a year, and you can start building datasets. You know the relation between all your Earth time measurements. Now start forming approximate connections - a sundial will tell you about the Alien day, and its hours, and its minutes. Does it take 60x60 seconds to cross a twelfth of the dial? Does this change in the morning or evening versus midday?
Exploit relations:
After a week you wont have a conversion chart, but you'll know if a day is longer here or not. You'll also be able to guess by about much, since that 'hour' happened too fast, or the nights lasts too long. The drift on your circadean rhythm will also help. If each morning comes too soon or not soon enough, or each evening, these are hints. If there are moons, track how long each one takes to drift across the sky, relatively. Do they make it from Alien-east to Alien west, or vice versa, before the ngiht ends? Do they make multiple passes?
Have the terrain tell you:
Observe the animals and plants and whatever else lives on this world. Draw relations between them and known creatures of Earth. 204
Are they larger? Smaller? Do trees have leaves all the way around, or do they favor a side. Which way to birds fly more often? There is an unending amount of data to be collected from the environment, ever living things adapted to life here, and can tell you how to survive given the natural time.
Put it all together.
You can count Alien days, hours, minutes. You can draw the relations. From there, you can guess about how many Aliens days equal 365 Earth days. Depending on how much skew you think you have, you can pad yourself which 5% or 10% earliness, or simply try to underestimate time so that you are guaranteed to arrive back early.
Example:
Counting off rough minutes, coupled with a 12-hour sundial shows that each hour is about a third longer than you think it should be. You observe a moonrise and moonset every night, which at least 30-60 minutes to spare on either side. That would lead to two or three tide cycles in a day, and you can chart that on any body of water. If its truly periodic, you can find out roughly what time of day it is that way too. Both together and you can guess that a day is about 30-32 hours; you have about 273-292 Alien-days to wait. If either method contradicts the other, observe more and take more data, averaging the two.
Go Explore!
Now that you have a general timetable, go enjoy the local scenery and try not to get detained or captured. Also, they might be able to sharpen your time-conversion, or at least provide some paper so you can write all this down. Good Luck! 204