What you need to qualify
You need 6 Master professions, 5 exploration badges and completion of An Echo in the Sand to qualify. That's the custom quest starting with the dying Twi'lek on Tatooine. It replaces the old themepark requirement for Elder Haven's Jedi path.
An Echo in the Sand
A dying Twi'lek on Tatooine asks you to find her sister. The quest follows what happened to them, with some investigation, dangerous encounters and unfinished business along the way. It has its own journal and gives Adventure Insight XP.
/waypoint 4080 -4550 in chat. Follow it and look nearby for Zyanna, the dying Twi'lek. Once you meet the entry requirements, speak to her to begin.Finishing the story completes this part of the Jedi requirements. I'll leave the rest of the story for you to find out.
After qualifying
Once you qualify, you continue with the Old Man encounter and Force Sensitive progression. The long waits and Village phase delays have been removed.
At the Village, complete the required Force Sensitive training, face Mellichae and move on to the Padawan Trials. You can train the individual Force Sensitive branches without waiting for Village phases to rotate.
The Padawan and Jedi Knight Trials still follow their usual structure. The three Padawan hunting trials have nearby group objectives and waypoints. Your progress is saved, so you can come back and finish a hunt later.
Becoming a Padawan
When you become a Padawan, your non-Force professions are removed. From then on you can train Jedi and Force Sensitive skills, and ordinary profession trainers will refuse further training.
You keep your Insight, Prestige, equipment and completed story progress. Some Mandalorian and Smuggler activities need their profession skills, so keep that in mind before becoming a Padawan.
Your training equipment
The Training Lightsaber has two crystal slots, so it fits both a color crystal and your Padawan Crystal. Tune the Padawan Crystal before you put it in.
The Padawan crystal and robe are starter gear. The robe has modest defenses and Jedi Toughness, with no Saber Block bonus. You can get stronger equipment as you continue progressing.
Professions & Combat explains equipment bonuses and defenses. Insight / Prestige covers how you keep building your attributes.
More work on Jedi during alpha
As a Jedi, you can master all Force skill trees. There's still more work to do on Jedi gameplay and mechanics, and I plan to keep adding to them and improving them as alpha goes on.