What can I do with data from a data set if it is clearly non-normal?
You can still use center and spread measures.
If the graph (or bar chart) is very askew, the mean may not be a good center measure. If there is a clear peak in your values, you may want to consider the mode (which value occurs most often)..
The median is also a good measure, because it gives the midpoint of your cases (half is lower, half is higher).
Dependant on the number of data values you can refine this even further.
After you order the data according to value, you can pick out values on the 25%, 50% and 75% points, which will give you the first quartile
The difference between
If you have a lot of data, you can even refine this into percentiles, in which you cut up your data in 100 'bins' of 1% each.