What to do
Confirm the new departure time in writing and ask the airline what care they will provide tonight - hotel, meals, or transport to a nearby place to sleep. At the same time check whether any earlier flights still exist with other carriers on the same route or via a nearby airport. Decide if you need to arrive by a hard deadline tomorrow or if a few extra hours will still work. Keep every message and every receipt.

Three options
First option is to stay with the airline’s new flight tomorrow. This is the simplest path. You wait out the night, show up for the rebooked departure, and keep the original ticket value. Travel time the next day stays close to the planned duration, usually two to five hours depending on the route. The extra cost is mainly the night itself if the airline does not cover a hotel.

Second option is an overnight train if one still runs between the same cities or nearby stations. Some corridors have evening or night services that arrive early the next morning. Total travel time can be six to ten hours, but you sleep on the way and avoid the airport in the morning. Tickets bought at short notice often cost between 50 and 140 euros or dollars.

Third option is a combination of a late bus and an early local connection, or simply a full overnight bus. This works when trains are full or the rail link is weak. Journey time stretches longer, sometimes eight to twelve hours, yet the price stays lower, often 30 to 90 euros or dollars for a seat. You arrive later in the day but still move forward.

Cost
The airline rebooking itself is usually free when the delay is on their side. Hotels and meals may be covered if the delay is long enough and within their control, but this is not automatic. Anything you buy yourself - train, bus, extra night - comes from your pocket first. Save every receipt because some of those costs can be claimed later.

How to protect the rest of your trip
Message anyone you were supposed to meet tomorrow and give them the new realistic arrival window. If you had a hotel or rental car on the other end, write to them tonight and shift the booking if possible. Keep the original flight cancellation or delay notice, it helps with any later claims. If you choose a train or bus, photograph the ticket and the boarding point so you have proof of the alternative you took.

Summary
A delay that slides into tomorrow is inconvenient but rarely leaves zero choices. Confirm what the airline will cover for the night, then compare their next flight against overnight trains and buses. Pick the path that gets you there with the least damage to the following days, keep every receipt, and update the rest of your plans before you sleep. Most people who run these checks tonight still arrive in reasonable shape the next day.