The patch notes detail how the new system is designed to work, and it's a pretty typical queue system. When there's high demand, everyone will get to the queue screen after the title screen, with a number showing your place in the virtual line. You'll have the choice to leave the queue and play offline if you wish or simply wait for an opportunity to log in.
While login queues are an imperfect solution that doesn't seem to be winning over some frustrated players, using queues is just one of their multiple step approach to helping those that bought the game to get in and play without progress loss or being kicked out. Since the login troubles that have affected the game since launch day are due to several factors, including basing the game on the original code, queues aren't ideal but they should help monitor demand and lend some breathing room for the other fixes to come.
Diablo II: Resurrected's launch perhaps does have some potential lessons in the use of older code and in maybe planning cross-platform and cross-progression releases, but the community should have some help in getting into the game for the time being. Of course, wait times are not limited to older ARPGs like this one, and they can happen with demand spikes, It still remains to be seen how their other planned changes will play out. Still, maintaining server demand levels are at least something that is actively assisting for the time being in the hopes of keeping things more stable. Check out the patch notes and details on the update here.