Okay, so here is what i have found out from my own personal online research. I hope this helps.
So far, from what i have read online, at least in a few states, the process is pretty straightforward. You just take your expiring DL, EAD and the Federal Notice of automatic extension to the DMV and they should be able to provide you with a DL with an expiration date of 03/24/2020 (which is till when the TPS is extended). States under this category would be TX, ND and OH.
Having said that, most of the times, it seems, the process is not so easy, unfortunately. I have seen people give different accounts based on various factors like if it's a Red (republican) and Blue (democratic) state, if DMV is in an urban or rural area, etc. I have also read people resorting to applying for an EAD (even though it is automatically extended) just so that they don't have to go through all the hassle that comes with this confusion (imagine the hassle).
So, what's the bottomline? What should you bring to the DMV? Following steps should be obvious and should be able to help, i think:
Must Haves:
1. Gather your current (soon to expire) DL.
2. Gather your current (soon to expire) TPS EAD.
3. FEDERAL NOTICE of automatic extension (most important).
Supplementals:
4. Be prepared to talk to the DMV officials. Talk to a senior officer, if the junior staff (the person at the window) is not being able to help you. Be calm and explain your situation to them.
5. There is something called SAVE created by USCIS. Your state/DMV might participate in this and might be able to honor it's results (your are in luck, if they do). Be sure to talk about this feature if they don't bring this option up first.
Probably do this like right now or today:
6. Call or visit your DMV well ahead of time and find out about what they accept and need.
I have been able to reach the website off and on throughout the day. Interestingly, sometimes it works better in mobile and sometimes better on computer.
Not sure if this helps but here is another link to try:
https://www.dvlottery.state.gov/ESC/
