- What does the expansion contain?
- What are the different ways to play with it?
- How is each different from playing without the expansion?
- Is there anything else I should know about the expansion before buying?
The primary mechanical change is an alternate set of tickets, and there is also an additional bonus score condition.
The tickets work exactly the same way as normal, but it's a different set. They may also be combined into a single large ticket deck.
The standard bonus condition is longest route; the new one is most completed tickets. Both have the same value, and are often not the same person.
Since I've only played 1910 online, I can't speak to the card size issue.
Europe 1912, the comparable expansion for Ticket to Ride: Europe, likewise has replacement tickets and the most routes bonus, but instead of adding full size cards, instead adds a "depot" mechanism, which results in the trains deck being depleted sooner and more cards being out of play. While the tickets are not cross-compatible, the depots are. Since TTRE also has separate long route cards, 1912 also adds 6 more, to a total of 12.
I'll let someone else explain the expansion options, I just want to list the most important change.