I don't own a watch, and don't have a clock in my room. If I'm out and about, I could either look at clocks (found in classrooms, banks, on top of towers, etc.), look at other people's watches (which requires a little skill in mental rotation), or look at something I have which has a clock (laptop, camera, etc.).
Although I usually leave my laptop on when I sleep, I blank the screen so it doesn't brighten the room at night. If I wake up but don't feel like getting out of bed yet, I can't really tell from my laptop what time it is.
Instead, I've sort of trained myself to get a rough idea of the time by looking at what color the ceiling is, and how big a difference in brightness there is between the window "shadow" and the rest of the ceiling. If it's dark all round, it's probably before 6:00. 7:00 or so is a little lighter, but the contrast is not that big, as the sun is not up yet. The largest contrast is about 7:30 to 8:00, when there are actual lines delineating the window "shadow". Past that, the room keeps getting brighter, while the contrast disappears, until past 9:30 or so when the room is comfortably well lit through the curtains.
An alarm clock would probably be less work, but this works too.