felt like trying to think logically about it would make it less random so immediately committed to the first number that came to mind which was 3

I envisioned spinning a wheel with sectors labeled 1-10 several times and ended up at 8.

I saw this and thought six seven in 10 milliseconds.

Counted the number of words of this post I could definitely remember

Thought even numbers were more likely to be picked (which was true at the time I voted, 17 to 13), small numbers less likely (also true, by the same ratio), and 1 and 5 are too round. And I hit the last unpicked number.

I decided to take a digit from the decimal representation of pi at the 20th place. (I have ~50 digits memorized from a competition with a friend many years ago.)

I did not internalize the question very carefully before closing my eyes to think, so if you'd been asking for a selection out of eleven options (0-10) my method wouldn't have been very good!

184 (arbitrary) mod 7 (arbitrary) x 2 (arbitrary) = 4

I meditated on it and four called out to me

@MaxE the meditation lasted like 5 seconds*

I thought of a poem/sentence that has a lot of words and counted them, resetting back to 1 after 10.

I just thought some numbers that felt random that added up to ~50 and took the ones place. I usually do mod 3 if I can find a way to involve it because it's hard to figure out what numbers are mod 3 but easy to verify in your head

Added together all numbers between 10 and 1 and took the last digit

It seems people are not following the instruction to explain their method here in the comments.

I thought that following Benford's law, 9 would be under represented, so in aid of reskewing to random...

@JussiVilleHeiskanen doesnt benfords law only apply to datasets with large variation over orders of magnitude

I initially thought about visualizing dice rolls or something, but instead I decided to take as many meaningful numbers as I could think of (my birthday, other important dates, my apartment number, references to things, etc), add all the digits up, and pick the last digit + 1 (to make the range 1-10) as my random number.

I got 7 by doing this which felt unsatisfyingly unrandom but oh well, I'm not overriding my method after completing it

@Robincvgr I did something similar, but with fewer sources of data