They are both forms of irregular verb "do". "Did" is a past simple and "done" is a past participle. They are used in different tenses. Examples: I did a lot of work last year. (Past simple tense) I have done a lot of work recently. (Present perfect tense).

Done is the past participle of the verb "do", and did is the past simple of the verb "do".

A tabular representation of the above answers which maybe useful. http://www.verbix.com/webverbix/English/do.html