I am on the pill for birth control, but lately my period has been coming in the middle of the pack so I stopped taking the pill. And now I'm pregnant. How can I figure out when my ovulation day and conception day was?

They will use the first day of your last period to start with and then make any changes, if necessary, once you have a scan done to determine a due date.
Generally ovulation occurs midcycle, or about 12-16 days before a period starts, but this is not exact for everyone and since your periods were off from their norm, you will have to use your due date to count back to get a rough idea.

Is there an issue why you need to know conception dates, the doctor will have some educated guesses based on the info you give them on date of last period, and by size of the baby from the exam. But there is no "exact" date that will be 100 percent.