Hi Leah,
I don't have direct experience with SEER but I've imported data for other large, public datasets in ASCII format. You do need a data dictionary which tells Stata how to translate the numbers in an ASCII file into variables. The National Health Interview Survey provides a data dictionary in the form of a Stata do file to define the variables. Check to see if the SEER website (or wherever you got the ASCII file from) has a readily available do file that you could use.
As an alternate solution, I came across this website that includes the SEER data in various formats, including Stata dta files:
http://www.nber.org/data/seer_u.s._county_population_data.html
I'm not sure that these data are the most current or comprehensive, but may be worth taking a look at. Certainly better than needing to develop your own data dictionary!
Maria