Hi Mark,
Dates in the sports standings program are formatted as Unix timestamps. Basically, a Unix timestamp is the number of seconds since seconds January 1, 1970 for a particular date. For an idea on what these look like, see this post and enter some times into the generator.
There is probably an "export" function from Access. From there, you will have to massage the data to fit the data types of the destination database fields. There are many ways to do this — from importing into a separate MySQL table first, to manually working on the exported Access data to make it conform (this is probably best).
There might be a specific step-by-step process for your situation, but for that I or someone else would have to look at your Access database to see what's there, in what format, and what you want to import.