Century
First, you'd have to watch through a night to see if Polaris wobbles - currently, the radius is about 1° I think, but that changes with precession (and nutation, but that's small enough to ignore).
Once you know that, you can try to find a point in the sky that stays still all the time (like Polaris nearly does in our time). This is celestial pole, the direction the axis of earth points to. 188
It moves in a circle with ~23° radius ( = obliquity of the ecliptic, currenty ~23,4°). The center of the circle is roughly between Polaris and Vega, that makes it easy.
Then, you have to see whether Polaris is approaching or departing it on its way on the "precession circle".
If you can measure the angle $\alpha$ it has travelled on its way on this circle, you can estimate which century you have been transported to: $year = 2000 + \alpha \frac {26000} {360}$
If you take exact values and do all the calculations and especially the measurements very very exact, you might get more than just the century.
If you really want to prepare, print this and pin it somewhere you will see it every day: https://en.wikipedia.org/wiki/File:Precession_N.gif
Beware that if you are transported more than 13,000 years back or forth, you will guess wrong.
In this case, you'll have to take the proper motion of the stars into account - you'll have to know not only the sky but also the motion of the stars (or at least a few) very very good. Which is the first thing that is really hard to do.
Maybe you'd have to invent something with sticks for the measurements.
Year
I guess you need to know the planets positions (especially Jupiter because it's bright and not to fast) of the time you are transported to to derive the year - but you'd have to be a walking ephemeris for this.
Time of the year
The time of the year is actually much easier than the year - most of the time, you can even feel it.
If you still need to calculate it, it is a direct function of the position of the sun in the sky:
You need to know the orientation of the ecliptic in the sky and the equinox of our time - in Pisces, you can see it in the image in that Wikipedia link: the intersection of "0°" and the ecliptic.
You measure the time in hours $h$ that passes from either the spring or the fall equinox (of our time) is at midheaven until the sun is at midheaven (noon).
The current date of the year, measured (roughly) from january to december in values from 0 to 1 is: $ y = h/24-0.2+\frac \alpha {360}$
If you took the fall equinox, you have to add or substract 0.5, whichever fits.
Without the $-0.2$, it would be measured from spring equinox (~ march 23rd) to spring equinox.
Geographical latitude
The angle of the celestial pole mentioned above and the ground (as long as it's horizontal) helps you calculate the geographical latitude $ \phi = 90°-angle$.
Geographical longitude
Sorry, that's the thing I could not do. 204