The clock starts running for an appeal of a Texas state criminal trial court judgment when the judgment is signed. Usually its the defendant who appeals. If the defendant does not file a motion for new trial or a motion in arrest of judgment,a notice of appeal must be filed thirty days or less after judgment in the trial court. (Motions in arrest of judgment are very rare nowadays, because by statute, rule or precedent, all errors that I am aware of that would justify arresting a judgment either have to be objected to before judgment or would be open to correction by a motion for new trial or a writ of habeas corpus.). If a motion for new trial is filed, it must be presented to the trial court ten days or less after it is filed, unless the trial court gives permission for it to be presented sometime 75 days or less after the judgment is signed. If a motion requires a hearing, as it would if it were based on jury misconduct about which evidence would have to be taken, that hearing must take place 75 days or less after the judgment is signed. The notice of appeal may be filed 90 days after judgment if a motion for new trial, etc. was filed 30 days or less after the judgment was signed.
The State has 20 days to appeal if it wants to appeal a judgment no matter what else gets filed.
A docketing statement should be filed in the Court of Appeals when the notice of appeal is filed. Also, if the defendant be indigent, the defendant should file a motion for a free record and an affidavit of indigence.
The clerk's record is usually prepared relatively quickly, often a couple of weeks. Preparation of the reporter's record is usually a very time-consuming part of the appellate process, often taking months. The appellant's brief is due 30 days or less after the reporter's record is ready.