Measuring time

I don't really know how to explain it (or where to start or what to do)... I want to measure time, but not like we do. What I mean is, the years, they are not "2020; 2036" but also not the distant future, "4689" for example (or really really far back, like 1362).

Some other way to measure years. It's also called years but it's different from our years. It should be easy to use, meaning, not "87.476 sunrises" or something. Just like you tell someone that it's the year 2026 right now.

Any ideas? I also have nothing against longer explanations and "absurd" ideas. I will try my best to answer each comment (sooner or later!).