The following information is according to Bill Williams who is representing Florida State in its case against the NCAA:
The school has until April 23rd to submit the written appeal (next Thursday). They have not sent in the official appeal yet, Mr. Williams is not sure when that will happen, but it has to happen within the next 10 days.
Then, the infractions committee has 30 days from April 23rd to respond to the appeal.
From there, FSU then has 15 days to respond to the response from the infractions committee.
So, by mid to late June all the writing portions should be complete.
If FSU is dis-satisfied with the results, then they can appeal for a hearing in person before the committee and that could take months to plan and schedule.