"MRW"
I took some measurements of an AM broadcast from multiple points up to
about half a mile from the transmitter. The transmitter was supposed
to be operating at 20W. I don't know what kind of pattern the AM
antenna had, but can I just use the field strength readings that I got
to predict how far the signal can go out? I only was able to measure 3
points, but I want to know if that is sufficient to make an estimate
under the same conditions.

An estimate is possible, but assumptions will need to be made. If you can
post the readings you got, the path lengths, and the general location for
the transmit site I can give you some idea about that.

Of course if you can post the call letters of the station then the FCC data
for that station will show they should be.

If so, how do I go about starting this? Are there any formulas? Also,
on average AM receivers, what would be considered a minimum field
strength value that would yield an audible sound?

I also read that frequencxies less than 2MHz rely on surface waves. Is
there a site that I can visit that will give me an idea on how to take
this into account given that there are different ground
characteristics? Thanks!

The FCC publishes charts that may be used for this purpose. As for minimum
usable daytime field for a typical, cheap indoor receiver in an urban,
residential area, a value of 1 or 2 mV/m typically is needed.

RF http://rfry.org