How do we calculate the time it takes for the Earth to make one revolution on its own axis and of the sun?

Basically what I'm asking is how we know the length of one day and of one year. What precise instrumentation or calculation do we make use of that allows us to know these times to so many decimal places?

My best guesses:

• For one day, do we use the background stars as a reference point?

• For one year, do we calculate how long it takes us to return to that same distance from the sun (i.e.: to get back to .97 AU)?