Assemble your entire production team -- everyone from animators to the sound supervisor -- to break down the completed screenplay and budget draft. Discuss the project with your team on a scene-by-scene basis and break the production down into tasks and sub-tasks, making conservative estimates about how much time each scene will take to complete. Be sure to buffer your estimates with a little time for potential revisions and client feedback -- especially for any scenes involving special effects -- and possible technical snags. When you have worked your way through the entire script, write up a polished draft of the complete production schedule.
Meet again to discuss and revise the complete draft of the production schedule. Have you been conservative enough about time estimates? How much work can your team complete, realistically, in a week's time? Have you been too liberal about time estimates? If the project is 2D animation, make sure you've considered how reusable cycles -- e.g., for walks and runs -- will affect the delivery time. If the project is 3D animation, make sure you've included enough time for textures. Consider your overall budget and ask your team if outsourcing certain aspects of the production could help your schedule and your bottom line. Make adjustments as necessary.
Take the completed schedule and make it into a Gantt chart using a template downloaded from the Web, your spreadsheet editing application of choice or an open-source tool like GanttProject. Seriously consider using a Web-based project management tool -- whether freeware like dotProject or commercial like Basecamp -- with built-in support for Gantt charts. Having your production schedule and associated project plan in a central and easily-accessible location keeps your team on the same page about delivery dates and performance expectations, and enables everyone to make any necessary adjustments on the fly.